Question

Are the triangles similar? If so, write the similarity statement and state which theorem or postulate is used to prove the two triangles similar.

A.
Yes, ΔABC ~ ΔEDC by the SAS similarity theorem.
B.
Yes, ΔABC ~ ΔDCE by the SSS similarity theorem.
C.
Yes, ΔABC ~ ΔDEC by the AA similarity postulate.
D.
No, these triangles are not similar.

Answer 1

the answer would be D) no, these triangles are not similar. I'm pretty sure they would be similar if one of the answer choices said ΔABC ~ ΔCED

Answer 2

Answer: D. No, these triangles are not similar.

Explanation:

From the given picture, it can be seen that in Δ ABC, AB=BC=9 units

Therefore, ∠ABC=∠ACB=65° [Angles opposite to equal sides of a triangle are equal]

Then ∠BAC=180°-∠ABC-∠ACB [by angle sum property of triangle]

⇒ ∠BAC=180°-65°-65°

⇒ ∠BAC=50°

Similarly in ΔDEC, DA=DC=6 units, then ∠DEC=∠DCE [Angles opposite to equal sides of a triangle are equal]

Let ∠DEC=∠DCE=x

Then by angle sum property, in ΔDEC

∠DEC+∠DCE=180°-∠EDC

⇒ x+x=180°-46°

⇒ 2x=134°

⇒x=67°

∴∠DEC=∠DCE=67°

We can see that no two angles of both the triangles are equal.

Therefore, hese triangles are not similar.