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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

Practice Problem 7

and

3

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

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 :

Final answer:

To prove that the diagonals of an isosceles trapezoid are congruent, use the principle of congruent triangles. By drawing the diagonals AC and BD, we create two triangles ΔACD and ΔBCD. As ABDE is an isosceles trapezoid, and by the SAS postulate, the triangles (and thus the diagonals) are congruent.

Explanation:

In order to prove the diagonals of the isosceles trapezoid ABDE are congruent, we can use the properties of congruent triangles. First, draw diagonals AC and BD. By doing this, we form two triangles: ΔACD and ΔBCD.

As ABDE is an isosceles trapezoid, it implies that the non-parallel sides (AD and BE) are of equal length. Therefore, AB is congruent to DE. Additionally, angles BAC and EDA are base angles of the isosceles trapezoid and are thus congruent.

Now, noticing that CD is a common side to both triangles, we can say it's congruent to itself. Having all these in mind, we can say that ΔACD is congruent to ΔBCD due to Side-Angle-Side(SAS) postulate. Since diagonals AC and BD are corresponding parts of these congruent triangles, they are therefore congruent.

So, Priya is correct: diagonals of an isosceles trapezoid are indeed congruent.

Learn more about isosceles trapezoid here:

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