Given: ABCD is a parallelogram with AB parallel to CD and AD parallel to BC. Diagonal AC is congruent to diagonal BD. Prove: ABCD is a rectangle (angles A,B,C, and D are right angles).

Q: For another proof of the Pythagorean theorem, consider a right triangle ABC (with right angle at C)…

A: Since, according to our guideline we have to answer only first question. I am answering first one.…

Q: Given: DE AB, EC BC, 4B <E Prove: C is on the perpendicular bisector of AD Statements Reasons

A: Based on the Sides equality in the Hexagonal polygon, DE = AB and BC = CE Here angle according to…

Q: - equal rectangular lots are enclosed by fencing the perimeter of a rectangular lot and then putting…

A: let the length of the lots =L and breadth of the lots= x area of the lots = L×x It is given that…

Q: What triangle congruence postulate would prove that the two triangles are congruent? X. AAS SSS SAS…

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Q: What additional information is needed in order to prove that the triangles are congruent by the ASA…

A: Given,

Q: Use deductive reasoning to show that the two triangles are congruent Given that LFAB LGED and C is…

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Q: . In a convex quadrilateral ABCD, there are given ||AD|| = 7(√6 – √2), ||CD|| = 33 5 $³3³, and D =…

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: If DE is not parallel to BC, what is DE? 56 C DE %3D Submit

A: Solved below

Q: E H. en that EH=5, what is the length of HF?

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Q: 11. ABCD is a quadrilateral such that if sides AB and CD are extended they will meet at a right…

A: Solution: Consider the given quadrilateral ABCD and assuming line AB and CD extended and create a…

Q: Given kite ABCD and isosceles trapezoid WXYZ, complete a two-column proof to show that AADW = ACDZ.…

A: For the given Kite A B C D and Isosceles trapezoid W X Y Z  It is given that  AC is parallel to W Z…

Q: In the diagram of AABC below, DE || AB. C A If CD = 4, CA = 10, CE = x + 2, and EB = 4x- 7, %3D %3D…

A: We have given DE||AB in ∆ABC Then, By the triangle proportionality theorem: If a line parallel to…

Q: Calculate the area of a rhombus with sides measures 10 inches and a longer diagonal measuring 16…

A: 96 in^2

Q: if ABCD is a rhombus, AC=4, and ADC is an equilateral triangle, what is the area of rhombus?

A: Drawing the figure as per the question, As we are given that AC=4 and ADC is an equilateral…

Q: If a parallelogram is a rectangle, then its diagonals are a) perpendicular. b) congruent. c) none of…

A: diagonals are ?

Q: Determine the area of a quadrilaterals with incircles, having sides a = 9.66 m, b = 7.54, c = 11.44,…

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Q: Which two triangles are congruent by the SAS Theorem? Complete the congruend statement. R RST E DBC…

A: We have to check

Q: 40. As marked and with LH = LC, a) are quadrilaterals ABCD and EFGH congruent? b) is DC = EH?

A: Congruency of quadrilateral using congruency of triangle

Q: ABCD is a quadrilateral with AB equal and parallel to DC. Prove that AD is equal and parallel to BC.…

A: I hope you are asking for question 6. We solve the given problem using congruent triangles. SAS…

Q: Which postulate would prove the triangles congruent? R V U SS AAS ASA SAS

A: Correct Answer: (D) SAS Postulate

Q: Given: ZB is a right angle; AB || DE, Prove: ADEC is a right triangle. 1. Proof

A: 4. Statements Reasons ∠B is a right angle, AB∥DE Given. BC⊥AB Definition of rt. ∠. BC⊥DE If…

Q: In rhombus ABCD, with diagonals AC and DB, AD = 10. If the length of diagonal AC is 12, what is the…

A: Using the given information, draw a rhombus and label it. In a rhombus, the diagonals are…

Q: Given kite ABCD and isosceles trapezoid WXYZ, complete a two-column proof to show that AADW ACDZ. х.…

A: Kite ABCD and isosceles trapezoidal WXYZ. WD ≅DZ XB≅BY

Q: Complete the following statements. a. If AY SR= ANVD, then DV = ? and MZRYS =__? _ . b. If AB…

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Q: 2. Given: ABCD is a parallelogram, DE I AF, and CF 1 AF Prove: DE = CF D C Statement Reason A E

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Q: In concave quadrilateral ABCD, the angle at A measures 40°. AABD is isosceles, BĆ bisects ZABD, and…

A: Given: The value of Angle A measures 40°. The side BC bisect ∠ABD and DC bisect ∠ADB. The triangle…

Q: Prove that: If AD is the angle bisector of A (in triangle ABC), and if u = BD and v = CD, then ас U…

A: Given: AD is the angle bisector of angle A in triangle ABC.u=BD and v=CD To Find:  To prove that…

Q: Are quadrilaterals ABCD and EFGH congruent if: a) AB = EF, BC = FG, CD = GH, and AD = EH? b) AB =…

A: We are given two quadrilaterals ABCD and EFGH.We have to  check the congruency of two quadrilaterals…

Q: Given: LA and LC are right angles LABELCBD, AE CD Prove: BEBD C B E.

A: According to given,  By Angle Side Angle rule ΔABE is congruent to ΔCBD

Q: Suppose AABC is a triangle in the Euclidean plane and D is the point such that B*C*D and AD bisects…

A: Given:  AB=9AC=6CD=12 B*C*D means points B, C, Dare distinct and they lie on the same line.  B*C*D…

Q: In the given figure, PQRS is a parallelogram, whose diagonals PR and SQ intersect at O. If OR = 7.5…

A: it is given that 'OR' =7.5 cm

Q: the accompanying figure, ABCD is a trapezoid in which AD||BC and AD> BC. Prove that if AB CD, then…

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Q: Let AC and BD be two line segments that bisect each other at E, with AC & BD. Prove that ABCD......…

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Q: In the accompanying figure, ABCD is a trapezoid in which AD|BC and AD> BC. Prove that if AB=CD, then…

A: To prove the given angle

Q: AV 4. J 4a- If the triangles are congruent, write the name of the congruent triangles: 4b- If the…

A: To solve the congruency problem and state the postulate or Theorem.

Q: What type of trapezoid a) has congruent diagonals? b) has congruent base angles?

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Q: ABCD is a rectangle. a. If AB = 12, BC = 5 and AC= 13, find DC, AD and DB. b. If 21 = 35°, find…

A: As per Bartleby answering guidelines if a questions has multiple subparts then an expert is expected…

Q: Let AC and BD be two line segments that bisect each other at E, with AC & BD. Prove that ABCD......…

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Q: 7. Find the area of the quadrilateral if AB = 3, BD = 12, AC = 4, CD = 13, and AB is %3D…

A: Join BC

Q: 3. Given AABC AJFK, list all of the congruent angles. * ZB = ZJ, 2C= LF, LA= LK ZC = LF, ZA ZK ZB =…

A: Given: ∆ABC~∆JFK

Q: Given: E is the midpoint of AB and CD Prove: Triangle AEC is congruent to Triangle BED

A: from the above fingure,∠C≅∠D   and ∠A=∠B=90°   —Here, CA⊥AB and DB⊥AB   —CE=EDAs CD is…

Q: What value of I would prove that ray AB is an angle bisector of ZCAD? C (2x+10)B (x+ 15)°

A: Given that ∠CAB=2x+10  , ∠BAD=x+15   and Ray AB is angle bisector of ∠CAD   i.e ∠CAB=∠BAD   i.e…

Q: in ABCD, lines BH is perpendicular to AD and line BG is perpendicular to CD. How are ABH and CBG…

A: Given problem:-

Q: Which congruence theorem below would prove the triangles congruent? B A A) SS B) ASA C) AAS D) HL E)…

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Q: A В 丰 E D 丰 C. Note: DB and AC are segments.

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Q: In the diagram below of triangle ABC, D is a midpoint of AB and E is a midpoint of BC. If DE = 64 –…

A: As given D is midpoint of AB so BD=AB/2 As given E is midpoint of BC so BE=BC/2 Now using property…

Q: Type SSS, SAS, ASA, SAA, or HL to justify why the two larger triangles are congruent. C A AC = EC AB…

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Q: Given triangle ABC whose sides are AB = 15 in, AC = 25 in and BC = 30 in. From a point of side AB, a…

A: The solution of the problem is given in the next step.

Q: 7. Find the area of the quadrilateral if AB = 3, BD = 12, AC = 4, CD = 13, and AB is perpendicular…

A: 7) To find the area of quadrilateral ABCD Join the vertices B and C Triangle BAC and triangle CBD…