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Thank you for visiting Priya is convinced the diagonals of the isosceles trapezoid are congruent She knows that if she can prove triangles congruent that include the diagonals then. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!

Priya is convinced the diagonals of the isosceles

trapezoid are congruent. She knows that if she can prove

triangles congruent that include the diagonals, then she

will show that diagonals are also congruent. Help her

complete the proof.

ABDE is an isosceles trapezoid.

Draw auxiliary lines that are diagonals

2

AB is congruent to

segment. We know angle B and

congruent to

5

congruent because of

8

because

7

and

because they are the same

4

are congruent. We know AE is

Therefore, triangle ABE and

6

Finally, diagonal BE is congruent to

are

9

1

2

3

4

5

6

Priya is convinced the diagonals of the isosceles trapezoid are congruent She knows that if she can prove triangles congruent that include the diagonals then

Answer :

Priya's proof shows that all diagonals of isosceles trapezoid ABDE are congruent.

Given Information: We start with isosceles trapezoid ABDE, where AB is parallel to DE, and AD is congruent to BE.

Auxiliary Lines: Priya draws auxiliary lines to create diagonals. Diagonals AC and BD intersect at point X, forming four triangles: AXB, BXD, CXD, and CXA.

Congruent Sides: AB and DE are congruent due to being opposite sides of an isosceles trapezoid. Additionally, Priya mentions that angles B and E are congruent, which suggests that triangles ABX and DEX share an angle and two congruent sides (AX = DX because AD = BE).

Angle Equality: Triangles AXB and DEX have a shared angle at X (since AX and DX are both parts of diagonal BD). Furthermore, triangles CXA and CXD also have a shared angle at X (since CX and CX are both segments of diagonal AC).

Triangle Congruence: By applying the Angle-Side-Angle (ASA) congruence criterion, Priya can now conclude that triangles ABX is congruent to triangle DEX (due to angle congruence, side congruence, and shared side AX = DX).

Diagonals Congruence: Since triangle ABX is congruent to triangle DEX, their corresponding sides are also congruent. Specifically, this implies that diagonal AX is congruent to diagonal DX.

Final Step: Priya has now successfully demonstrated that diagonal AX is congruent to diagonal DX. However, by symmetry, the same argument applies to the other pair of diagonals, BC and CD. Therefore, all diagonals of trapezoid ABDE are congruent.

In conclusion, Priya's proof relies on demonstrating congruence between triangles that share the diagonals of the isosceles trapezoid ABDE. This congruence of triangles ultimately leads to the conclusion that the diagonals themselves are congruent.

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Thank you for reading the article Priya is convinced the diagonals of the isosceles trapezoid are congruent She knows that if she can prove triangles congruent that include the diagonals then. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!

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