Question

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.

Answer 1

Explanation:

To prove that ΔABC and ΔEDC are similar triangles, we need to show that their corresponding angles are congruent and their corresponding sides are proportional.

Given information:

Angles A and E are right angles (90 degrees).

AC = 4, AB = 3, BC = 5, DC = 15, DE = 9, and CE = 12.

Step 1: Show that corresponding sides are proportional:

We have:

AC / DE = 4 / 9

AB / DC = 3 / 15

BC / CE = 5 / 12

We notice that AC / DE, AB / DC, and BC / CE are all equal to 4 / 9. Therefore, the corresponding sides are proportional.

Step 2: Show that corresponding angles are congruent:

Angles A and E are both right angles (90 degrees). All right angles are congruent.

Step 3: Apply the SSS Similarity Postulate:

Since the corresponding sides are proportional, and the corresponding angles are congruent, we can apply the SSS (Side-Side-Side) Similarity Postulate to conclude that ΔABC ~ ΔEDC.

So, the correct statement is: 15 over 4 equals 12 over 9 equals 9 over 3 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.