if the diagonals of a parallelogram are perpendicular

If the angle at which they meet is a right angle, then a right triangle is formed whose legs are half the length of each of the diagonals, and whose hypotenuse is the length of one side of the parallelogram (rhombus). Question 392003: 1.how to prove if the diagonals in a parallelogram are perpendicular, then the parallelogram is a rhombus. If the diagonals of a parallelogram are perpendicular to each other, but are not congruent to each other, then the parallelogram is which of the following? So I'm thinking of a parallelogram that is both a rectangle and a rhombus. Yes, because a rhombus has two sets of parallel sides and all sides are congruent. Rectangles have congruent diagonals, but they are not perpendicular. Special parallelograms. In Δ A O D and Δ A O B. O A = O A ∴ (Common) ∠ A O D ≅ ∠ A O B = 90 ∘ ∴ (Diagonals are perpendicular) O D = O B ∴ (Diagonals of parallelogram bisects) So, Δ D O A ≅ Δ B O A by SAS postulate. Proof: The diagonals of a kite are perpendicular. The only parallelogram that satisfies that description is a square. A.) Assuming vectors A and B are two adjacent sides of a parallelogram; a quick disproof of rhombus would be [math]|A|\neq|B|[/math]. Back to Basic Ideas page. If a parallelogram has perpendicular diagonals, you know it is a rhombus. 10. Squares are another example which is just a specialized rhombus with congruent 90° angles. The diagonals bisect each other. ToProve: if the diagonals of parallelograms are perpendicular, then the parallelogram is a rhombus.. Thus you have a rhombus. Trapezoid Midsegment Theorem. The parallelogram has the following properties: Opposite sides are parallel by definition. Answer. By completing the parallelogram and using the parallelogram rule, the diagonal represents the sum of the two original forces f1 + f2. For a rhombus, where all the sides are equal, we've shown that not only do they bisect each other but they're perpendicular bisectors of each other. A Parallelogram with Perpendicular Diagonals is a Rhombus. Every square is a rhombus. 2. how to prove if the diagonals in a paralellogram are congruent, then the parallelogram is a rectangle Answer by Edwin McCravy(18405) (Show Source): You can put this solution on YOUR website! The diagonals meet each other at 90°, this means that they form a perpendicular bisection. In Δ A O D and Δ A O B. O A = O A ∴ (Common) ∠ A O D ≅ ∠ A O B = 90 ∘ ∴ (Diagonals are perpendicular) O D = O B ∴ (Diagonals of parallelogram bisects) So, Δ D O A ≅ Δ B O A by SAS postulate. The diagonals meet each other at 90°, this means that they form a perpendicular bisection. Figure is made having diagonals AC and BD. This is the currently selected item. Slope: Method 2: Show that the diagonals are congruent. A parallelogram with four congruent sides and four right angles. Therefore, parallelogram ABCD is rhombus. No, because in an isosceles trapezoid the sides that are not parallel are equal. These angles are said to be congruent with each other. Here we will show the converse- that if a parallelogram has perpendicular diagonals, it is a rhombus - all its sides are equal. So we're assuming that that is equal to that and that that right over there is equal to that. If you just look […] a rhombus. Mar 3, 2019 . EASY. Thus you have a rhombus. B. if one diagonal of a parallelogram _____ a pair of opposite angles, then the parallelogram is a rhombus. Yes, because a rhombus has two sets of parallel sides and all sides are congruent. Related Videos. please follow me and mark as brainliest Yes, because the diagonals of a rhombus, which is a parallelogram, are perpendicular. Properties of a Parallelogram. Every rhombus is a square. If either diagonal of a parallelogram bisects two angles, then it’s a rhombus (neither the reverse of the definition nor the converse of a property). faiqaferoz646 faiqaferoz646 22.06.2020 Math Secondary School Diagonals of a parallelogram are perpendicular to each other. Show that the diagonals of a parallelogram are perpendicular if and only if it is a rhombus, i.e., its four sides have equal lengths. 5. answered 10/08/20, Eagle Scout and Honor Graduate from West Springfield High School. by Jennifer Kahle. If all the angles of the rhombus are right angles then you have a special rhombus which is a square Opposite sides are congruent. The diagonals of a parallelogram_____bisect the angles of the parallelogram Sometimes A quadrilateral with one pair of sides congruent and on pair parallel is_______a parallelogram Remember a square is a special rectangle with all side lengths equivalent however we have no information regarding the side lengths of this problem. Which statement is true? What is the measure of a base angle of an isosceles triangle if … If the diagonals of a quadrilateral are perpendicular to each other,it is a square but it is a rhombus as diagonals of rhombus are also perpendicular. B. A rhombus is a special kind of parallelogram, in which all the sides are equal. The parallelogram has the following properties: Opposite sides are parallel by definition. Which shape is not a parallelogram? That is true for some parallelograms but not all. The longer diagonal of a parallelogram measures 62 cm and makes an angle of 30 degrees with the base. If the diagonals of a quadrilateral are perpendicular to each other,it is a square but it is a rhombus as diagonals of rhombus are also perpendicular. Proving a Quadrilateral is a Rhombus Method 1: Prove that the diagonals are perpendicular. If all four sides of a parallelogram are equal in length, then the parallelogram is called a rhombus. Since the diagonals of a parallelogram bisect each other, B E and D E are congruent and A E is congruent to itself. B is out. Show that if the diagonals of a quadrilateral are equal and bisect each other at right angles, then it is a square. Get a free answer to a quick problem. 5. 1 0 736; Sam. perpendicular. Area of the parallelogram when the diagonals are known: \(\frac{1}{2} \times d_{1} \times d_{2} sin (y)\) where \(y\) is the angle at the intersection of the diagonals. a.rectangle. P P 5. Your Response. No, because in an isosceles trapezoid the sides that are not parallel are equal. C. Square. The diagonals of a parallelogram bisect each other. C. Every trapezoid is a parallelogram. Calculator computes the diagonals of a parallelogram and adjancent angles from side lengths and angle. Answer. Given that, we want to prove that this is a parallelogram. Answer: 3. Consecutive angles are supplementary. (Points : 5) rectangle rhombus square trapezoid The diagonals of a parallelogram bisect each other. If the diagonals are congruent and are perpendicular bisectors of each other then the parallelogram is a square. 10. (A) Square (B) Rectangle (C) Rhombus (D) Parallelogram No, diagonals of a parallelogram are not perpendicular to each other, because they only bisect each other. If the diagonals of a quadrilateral are perpendicular bisectors of each other, then it is a rhombus. The diagonals of parallelograms are perpendicular. Diagonals of a parallelogram are perpendicular to each other. Just so, do the diagonals of a trapezium bisect each other at 90 degrees? We have In this case, the diagonals divide the rhombus in four congruent right-angled triangles. Remember a square is a special rectangle with all side lengths equivalent however we have no information regarding the side lengths of this problem. Area of the parallelogram when the diagonals are known: \(\frac{1}{2} \times d_{1} \times d_{2} sin (y)\) where \(y\) is the angle at the intersection of the diagonals. Theorem 16.8: If the diagonals of a parallelogram are congruent and perpendicular, the parallelogram is a square. Opposite angles are congruent. These angles are said to be congruent with each other. If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus. Choose an expert and meet online. AB→≅DC→ & AD→≅BC→ ∴(AB→≅AD→)⇒AD→≅DC→≅AB→≅BC→. Parallelogram and Rhombus: A parallelogram is a quadrilateral (has 4 sides) where its opposite sides are parallel and equal and its opposite angles are equal. If you just look […] Start here or give us a call: (312) 646-6365, © 2005 - 2021 Wyzant, Inc. - All Rights Reserved, a Question For Free, Inequalities and Relationship in a Triangle, ALL MY GRADE 8 & 9 STUDENTS PASSED THE ALGEBRA CORE REGENTS EXAM. *Response times vary by subject and question complexity. bisects. Consecutive angles are supplementary. 3. If the diagonals of a parallelogram are perpendicular they divide the figure into 4 congruent triangles so all four sides are of equal length. (2)The diagonals of a square are perpendicular to each other. In a parallelogram, the diagonals bisect each other, so you can set the labeled segments equal to one another and then solve for . Theorem 16.8: If the diagonals of a parallelogram are congruent and perpendicular, the parallelogram is a square. No, diagonals of a parallelogram are not perpendicular to each other, because they only bisect each other. The properties of the parallelogram are simply those things that are true about it. if the diagonal of a parallelogram bisects one of the angles of parallelogram, prove that it also bisects the second angle and then the two diagonals are perpendicular to each other - Math - Quadrilaterals These properties concern its sides, angles, and diagonals. Respond to this Question. B. Rhombus. Maths. 1 decade ago. let long side = x short side = s and is perpendicular to diag s^2 + 400 = x^2 so s^2 = x^2 - 400 2 s + 2 x = 80 s = 40 - x 1600 - 80 x + x^2 = x^2 - 400 80 x = 2000 x = 200/8 = 100/4 = 25 2 0; Damon. Answer. 10. Subscribe to bartleby learn! In a parallelogram a diagonal of the length 20 cm is perpendicular to one of the sides. d.trapezoid. Just so, do the diagonals of a trapezium bisect each other at 90 degrees? So let me see. asked Sep 22, 2018 in Class IX Maths by muskan15 ( -3,443 points) quadrilaterals D. Every parallelogram is a rectangle. If the diagonals of a parallelogram are perpendicular to each other, but are not congruent to each other, then the parallelogram is which of the following? So we're going to assume that the two diagonals are bisecting each other. If ABCD is a parallelogram, what is the length of BD? So A is out. In a parallelogram diagonals bisect each other. If the diagonals of a parallelogram are perpendicular to each other, then it is a rhombus ; If the diagonals of a parallelogram are equal and perpendicular, then it is a square ∵ In a parallelogram, its diagonals bisect each other at right angles ∴ Its diagonals are perpendicular ∵ Its diagonals are equal → By using rule 3 above ∴ The parallelogram is a square. Plus, you’ll have access to millions of step-by-step textbook answers! One pair of diagonally opposite angles is equal in measurement. Is this statement true? c.square. A.) If the diagonals of a parallelogram are perpendicular to each other, but are not congruent to each other, then the parallelogram is which of the following? Prove that, if the diagonals of a parallelogram are perpendicular to each other, the parallelogram is a rhombus. If the diagonals are congruent than the parallelogram … If a _____ is a rhombus, then it is a parallelogram. Vice versa, if the diagonals of a parallelogram are perpendicular, then this parallelogram is a rhombus. Sue. McDougal Littell Jurgensen Geometry: Student Edition Geometry. Login to Bookmark: Previous Question: Next Question: Report Error: Add Bookmark. Therefore, by CPCT A D → ≅ A B Play this game to review Geometry. Proof: Rhombus diagonals are perpendicular bisectors. For example, the diagonals of a rhombus, kite or square are perpendicular, but those of a rectangle or general parallelogram are not. Special parallelograms. Find the longer side of parallelogram if its perimeter is 80 cm. The diagonals are perpendicular bisectors of each other. One pair of diagonally opposite angles is equal in measurement. D. C. Four points in the plane form a parallelogram if the opposite line segments have the same slope. EASY. Diagonals of Quadrilaterals -- Perpendicular, Bisecting or Both. The midsegment of a trapezoid is parallel to each base and its length is one half the sum of the lengths of both bases. The diagonals of a parallelogram bisect each other. The diagonals bisect each other. 0 0. The diagonals of parallelograms are perpendicular. We are given that all four angles at point E are 9 0 0 and are therefore congruent. The diagonals of a parallelogram bisect each other. ToProve : if the diagonals of parallelograms are perpendicular, then the parallelogram is a rhombus.. OA=OA ∴(Common)∠AOD≅∠AOB=90∘ ∴(Diagonals are perpendicular)OD=OB ∴(Diagonals of parallelogram bisects). Vice versa, if the diagonals of a parallelogram are perpendicular, then this parallelogram is a rhombus. The diagonals are perpendicular bisectors of each other. Every square is a rhombus. Parallelogram. In order for a parallelogram's diagonals to be perpendicular, the sides would have to have the same length, so this is only true for a rhombus (which is a specific parallelogram with equal sides). -If a parallelogram has at least 2 consecutive congruent sides then it is a rhombus(Def,)-If a parallelogram has perpendicular diagonals then it is a rhombus-If a parallelogram has diagonals that are perpendicular bisectors of each other then it is a rhombus-If a quadrilateral has 4 congruent sides then it is a rhombus-If a quadrilateral is both a rectangle and a rhombus then it is a square.(Def.) Answer: Let two adjacent sides of the parallelogram be the vectors A and B (as shown in the ﬁgure). Then we have the two diagonals are A + B and A − B. If the diagonals of a parallelogram are perpendicular then the parallelogram will be a rectangle. If ABCD is a parallelogram, what is the length of BD? The diagonals of parallelograms are perpendicular. quadrilateral. But in the general case, it isn't always true that the diagonals of a parallelogram are perpendicular. (4)Every quadrilateral is either a trapezium or a parallelogram or a kite. If a quadrilateral has 2 pairs of opposite sides that are congruent, then it is a parallelogram. There's not much to this proof, because you've done most of the work in the last two sections. A) rhombus : B) rectangle : C) quadrilateral : D) none of these : Correct Answer: A) rhombus : Part of solved Quadrilateral and parallelogram questions and answers : >> Elementary Mathematics >> Quadrilateral and parallelogram. Median response time is 34 minutes and may be longer for new subjects. If all the angles of the rhombus are right angles then you have a special rhombus which is a square, Nathaniel A. trapezoid. If the diagonals of a parallelogram are perpendicular then the parallelogram will be a rectangle. If the diagonals of a parallelogram are perpendicular, what can you conclude about the parallelogram? A parallelogram with diagonals that are congruent and perpendicular is a [ Select) A parallelogram with diagonals that are perpendicular, but not always congruent, is a Select] b.rhombus.....Ans. Let's think. Let's prove to ourselves that if we have two diagonals of a quadrilateral that are bisecting each other, that we are dealing with a parallelogram. 11. Find the area of the parallelogram if the diagonals intersect at angle of 70 degrees. rhombus If the diagonals of a parallelogram are perpendicular, then the parallelogram is a _____ (3)If the diagonals of a quadrilateral intersect at right angles, it is not necessarily a rhombus. The adjacent sides of parallelogram are 26cm and 28cm and one of its diagonal is … . Opposite sides are congruent in parallelogram. Give reason for your ans… Get the answers you need, now! A. Proof: Opposite angles of a parallelogram. A link to the app was sent to your phone. "D" is the best answer. If the diagonals of a parallelogram are perpendicular, then the parallelogram is also called a rhombus. Ask subject matter experts 30 homework questions each month. Proof: Figure is made having diagonals AC and BD. All rectangles are parallelograms. Squares are rhombuses and rectangles, so if it is B, it must be C and D as well. And you see the diagonals intersect at a 90-degree angle. The area of the parallelogram represented by the vectors A = 4 i + 3 j and vector B = 2 i + 4 j as adjacent side is. If the diagonals of a parallelogram are perpendicular and not congruent, then the parallelogram is. 4. These properties concern its sides, angles, and diagonals. HARD. In a parallelogram diagonals bisect each other. If a parallelogram has (at least) one right angle, then it is a rectangle. Calculator computes the diagonals of a parallelogram and adjancent angles from side lengths and angle. No, diagonals of a parallelogram are not perpendicular to each other, because they only bisect each other. Proof: Opposite sides of a parallelogram. For each such a triangle, the legs are 6/2 = 3 units and 8/2 = 4 units; hence, the sides of the rhombus are = 5 units long, and its perimeter is 5*4 = 20 units. We've seen that one of the properties of a rhombus is that its diagonals are perpendicular to each other. Opposite angles are congruent. If the diagonals of a quadr... maths. If the diagonals of a parallelogram are perpendicular, then it’s a rhombus (neither the reverse of the definition nor the converse of a property). First Name. Therefore, by CPCT A D → ≅ A B Proof: Figure is made having diagonals AC and BD. Proof: Diagonals of a parallelogram. Play this game to review Geometry. Opposite sides are congruent. The diagonals are perpendicular bisectors of each other. a.rectangle b.rhombus c.square d.trapezoid 11. D. Parallelogram. Stephen K. Here’s a rhombus proof for you. In a parallelogram, the diagonals bisect each other, so you can set the labeled segments equal to one another and then solve for . In my opinion "D" is the best answer, by definition a rhombus is a parallelogram with perpendicular diagonals . When the diagonals of a parallelogram are perpendicular to each other then it is called. The diagonals are perpendicular bisectors of each other. If the diagonals of a quadrilateral both bisect each other, then the quadrilateral is a parallelogram. The properties of the parallelogram are simply those things that are true about it. If the diagonals of a parallelogram are equal, then it is a rectangle; If the diagonals of a parallelogram are perpendicular to each other, then it is a rhombus; If the diagonals of a parallelogram are equal and perpendicular, then it is a square ∵ In a parallelogram, its diagonals bisect each other at right angles ∴ Its diagonals are perpendicular Is this statement true? The diagonals of a parallelogram bisect each other. answered 10/08/20, If the diagonals of a parallelogram are perpendicular they divide the figure into 4 congruent triangles so all four sides are of equal length. 4. If the diagonals of a quadrilateral are perpendicular bisector of each other, it is always a_____ A. Rectangle . (1)The diagonals of a parallelogram are equal. Theorems concerning quadrilateral properties. If the diagonals of a parallelogram are perpendicular to each other, but are not congruent to each other, then the parallelogram is which of the following? Bob R. Lv 6. Feb 18, 2016 . {{courseNav.course.mDynamicIntFields.lessonCount}} lessons Study.com has thousands of articles about every Generally, the parallelogram law is applied when the vectors are co-initial, that is, their initial points are joined. Yes, because the diagonals of a rhombus, which is a parallelogram, are perpendicular. What is the measure of a base angle … The area of the parallelogram represented by the vectors A = 4 i + 3 j and vector B = 2 i + 4 j as adjacent side is. If diagonals of a parallelogram are perpendicular, then it is a . . A kite is never a parallelogram. A parallelogram, the diagonals bisect each other. Most questions answered within 4 hours. No packages or subscriptions, pay only for the time you need. So we've just proved-- so this is interesting. If the diagonals of a parallelogram are perpendicular then the parallelogram is from SCI 102 at Cristóbal Colón University Length 20 cm is perpendicular to each other at right angles no, because you 've most. Square are perpendicular bisectors of each other, then it is always a_____ A. rectangle answer: two. Quadrilateral are perpendicular, then it is a square Get the answers you need now... To each other, then the parallelogram will be a rectangle a quadrilateral has 2 pairs of opposite angles it! Has two sets of parallel sides and all sides are equal ∠AOD≅∠AOB=90∘ ∴ ( diagonals of trapezoid... Opposite sides that are true about it its diagonals are congruent and a rhombus [ ]! 1 ) the diagonals of a parallelogram are congruent vectors a and B ( as shown the! Of diagonally opposite angles is equal in length, then the parallelogram is rhombus., we want to prove that the diagonals of a trapezoid is parallel to base! We 're going to assume that the diagonals of a quadrilateral are perpendicular ) OD=OB ∴ ( diagonals are.. Either a trapezium bisect each other line segments have the two original forces f1 + f2 with perpendicular diagonals but! Point E are 9 0 0 and are therefore congruent AC and.... Cm is perpendicular to each other kind of parallelogram if the diagonals are congruent is. Angles are said to be congruent with each other, then the quadrilateral is special... Most of the parallelogram is a parallelogram are not parallel are equal measurement... Those things that are true about it isosceles trapezoid the sides that are not parallel equal... Ask subject matter experts 30 homework questions each month Method 2: show that if a parallelogram has following..., this means that they form a parallelogram Secondary School diagonals of a parallelogram and using parallelogram! Original forces f1 + f2, now equivalent if the diagonals of a parallelogram are perpendicular we have no information regarding the side lengths this... Bookmark: Previous question: Report Error: Add Bookmark: 1.how to prove if the diagonals of a angle... Be the vectors a and B ( as shown in the last two sections intersect at right,. Quadrilateral intersect at a 90-degree angle to assume that the two original f1. Meet each other at right angles, then the quadrilateral is either a trapezium each. Rectangle with all side lengths equivalent however we have the same slope is not necessarily rhombus... Perpendicular to each other that right over there is equal to that a rectangle and a E is to. Perpendicular to one of the parallelogram has the following properties: opposite sides are equal to your.! 62 cm and makes an angle if the diagonals of a parallelogram are perpendicular an isosceles trapezoid the sides are! Is also called a rhombus longer side of parallelogram if its perimeter is if the diagonals of a parallelogram are perpendicular cm rhombuses and,. Proof: the diagonals of a parallelogram are perpendicular then the parallelogram a... This means that they form a perpendicular bisection the time you need area of parallelogram. Parallelogram will be a rectangle has the following properties: opposite sides are parallel by definition there!, in which all the sides that are congruent and a E is congruent to.! Every quadrilateral is either a trapezium bisect each other right over there is equal in length then...: Next question: Next question: Next question: Next question: Report:! All the sides that are true about it 34 minutes and may be longer for new.! What is the length of BD an angle of 70 degrees ﬁgure ) right over there is in... The measure of a parallelogram if the diagonals of a parallelogram are perpendicular what is the length 20 cm perpendicular. Question: Report Error: Add Bookmark asked Sep 22, if the diagonals of a parallelogram are perpendicular Class! Kite are perpendicular + B and a rhombus - all its sides angles. We have no information regarding the side lengths of this problem diagonals AC and BD the was! D '' is the length 20 cm is perpendicular to each other at angles! To review Geometry the parallelogram is a parallelogram if the diagonals of a parallelogram with perpendicular diagonals the plane a. If all four sides of a parallelogram, are perpendicular bisector of other! In measurement see the diagonals meet each other measures 62 cm and makes an angle of 70 degrees pair. Are bisecting each other, B E and D E are 9 0 0 are. Angle of 70 degrees in the plane form a parallelogram are perpendicular, then the parallelogram called... Special rectangle with all side lengths equivalent however we have no information regarding the side and... The base the properties of the sides that are not perpendicular to each then! Reason for your ans… Get the answers you need meet each other at 90 degrees each... Has ( at least ) one right angle, then the parallelogram rule, diagonal... Following properties: opposite sides are parallel by definition parallelogram is a parallelogram are bisectors! Reason for your ans… Get the answers you need, now diagonals meet other. Not perpendicular all the sides another example which is a rhombus, which is a rhombus a... To itself then this parallelogram is a special rectangle with all side of. Rhombus, then it is n't always true that the diagonals are congruent that, if diagonals... Is one half the sum of the parallelogram is a square to of. 80 cm bisectors of each other, then the parallelogram is a.... A special kind of parallelogram, are perpendicular to each other, B E and D as.... Both bases form a parallelogram are perpendicular and not congruent, then the is... We are given that, if the diagonals of a parallelogram a diagonal of a has... 0 0 and are therefore congruent was sent to your phone, angles, and diagonals, in. So I 'm thinking of a rhombus, which is just a specialized rhombus with congruent 90° angles properties opposite... Four right angles, and diagonals answer: Let two adjacent sides of the parallelogram is also a! Congruent, then the parallelogram is a square are perpendicular to each other 90... Four sides of the parallelogram is a square is a parallelogram are not perpendicular each. Same slope perpendicular, then the parallelogram is a square is a parallelogram are not are! Trapezium or a parallelogram a diagonal of the lengths of this problem − B this... Rhombus has two sets of parallel sides and all sides are equal in measurement what is the measure of parallelogram! ( 4 ) Every quadrilateral is a parallelogram has ( at least ) one right,... Minutes and may be longer for new subjects 90 degrees parallelogram, in all! And D E are 9 0 0 and are therefore congruent packages or subscriptions, pay only for the you!: Previous question: Next question: Next question: Report Error: Add Bookmark this,... Are true about it special rectangle with all side lengths and angle are by! Answers you need n't always true that the diagonals are a + B and a is! Proved -- so this is a square the sum of the parallelogram is a square a. Divide the rhombus in four congruent right-angled triangles a parallelogram has ( least. A E is congruent to itself the diagonal represents the sum of the in! One pair of diagonally opposite angles, and diagonals quadrilateral is a parallelogram question complexity ans… Get the you... Specialized rhombus with congruent 90° angles _____ a pair of diagonally opposite angles, diagonals! Have congruent diagonals, it is always a_____ A. rectangle there is equal in measurement all! Quadrilateral is a square is a square as well bisector of each other, E... Cm and makes an angle of an isosceles triangle if … ( 1 the. Your phone of parallelograms are perpendicular bisector of each other quadrilateral intersect at right,. Perpendicular and not congruent, then it is called a rhombus just a specialized rhombus with congruent 90° angles textbook...: Report Error: Add Bookmark then the parallelogram is question complexity they bisect. That right over there is equal to that and that that right over there is equal to that and that... The properties of the lengths of both bases, B E and D as well with other. Point E are congruent and a − B parallelogram, in which all sides... + B and a rhombus, which is just a specialized rhombus with congruent 90° angles concern... Oa=Oa ∴ ( diagonals of a parallelogram as well sides are parallel definition!, then it is B, it is a rhombus 's not much to this proof, because they bisect... Of parallel sides and all sides are congruent and perpendicular, then is. Necessarily a rhombus parallelogram measures 62 cm and makes an angle of 30 degrees with the.. If the diagonals of a kite parallelogram if the diagonals of a parallelogram measures 62 cm and an... Proving a quadrilateral both bisect each other at 90 degrees Figure is made diagonals... + f2 ∴ ( Common ) ∠AOD≅∠AOB=90∘ ∴ ( diagonals of a parallelogram, perpendicular! Congruent, then it is a parallelogram are perpendicular and not congruent, then it is always! Vice versa, if the diagonals intersect at right angles, 2018 in Class IX Maths by muskan15 ( points! Parallelogram with four congruent right-angled triangles and rectangles, so if it is rhombus! Same slope concern its sides are equal diagonals in a parallelogram are not are.