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Prove that ΔABC and ΔEDC are similar.

triangles ABC and DEC where angles A and E are right angles, AC equals 4, AB equals 3, BC equals 5, DC equals 15, DE equals 9, and CE equals 12

15 over 4 equals 12 over 5 equals 9 over 3 shows the corresponding sides are proportional; therefore, ΔABC ~ ΔEDC by the SAS Similarity Postulate.

∠E and ∠A are right angles; therefore, these angles are congruent since all right angles are congruent. 15 over 5 equals 12 over 4 shows the corresponding sides are proportional; therefore, ΔABC ~ ΔEDC by the SSS Similarity Postulate.

∠E and ∠A are right angles; therefore, these angles are congruent since all right angles are congruent. 12 over 4 equals 9 over 3 shows the corresponding sides are proportional; therefore, ΔABC ~ ΔEDC by the SAS Similarity Postulate.

∠DCE is congruent to ∠BCA by the Vertical Angles Theorem and 15 over 5 equals 12 over 4 shows the corresponding sides are proportional; therefore, ΔABC ~ ΔEDC by the SSS Similarity Postulate.

∠DCE is congruent to ∠BCA by the Vertical Angles Theorem and 15 over 5 equals 12 over 4 shows the corresponding sides are proportional; therefore, ΔABC ~ ΔEDC by the SSS Similarity Postulate.

Step-by-step explanation:

Answer Link

jainveenamrata jainveenamrata · Answer 2 · 2022-07-14T11:14:23+02:00

The triangles ΔABC ~ ΔEDC by the SAS Similarity Postulate. Then the correct option is C.

What is the triangle?

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

The triangles ABC and DEC where angles A and E are right angles, AC = 4, AB = 3, BC = 5, DC = 15, DE = 9, and CE = 12.

∠E and ∠A are right angles; therefore, these angles are congruent, since all right angles are congruent.

12 over 4 equals 9 over 3 shows the corresponding sides are proportional; therefore, ΔABC ~ ΔEDC by the SAS Similarity Postulate.

Then the correct option is C.

More about the triangle link is given below.

https://brainly.com/question/25813512

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