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.

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.

let's fu(!

step-by-step explanation: