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.

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schlosser1313 schlosser1313 · Answer 1 · 2017-03-23T16:44:52-04:00

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

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JeanaShupp JeanaShupp · Answer 2 · 2019-03-20T06:14:07-04:00

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

Step-by-step 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.