bleedingtrapdoor
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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.

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 b class=

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schlosser1313
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
JeanaShupp

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.

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