Question

Determine whether the triangles are similar. If so, write a similarity statement and name the postulate or the theorem you used. If not, explain.

Answer 1

The first pair of triangles are similar.

Triangle ABC is similar to Triangle PQR.

I used the SSS theorem of congruency.

( side - side - side) since I knew the sides were equal I knew that they were congruent.

----------------------------------------------------------

The second pair of triangles are similar too.

Triangle ABC is similar to Triangle DEF.

I also used the SSS theorem of congruency.

Since I knew what the sides were, I did some calculations and they all equalled 6...

----------------------------------------------------------

I hope that helps you out!! Any more questions??

Answer 2

Answer:  Both the pairs of triangles (a) and (b) are similar.

(a) By AA similarity statement.

(b) By proportionality statement.

Step-by-step explanation:  We are given to check whether the pairs of triangles in cases (a) and (b) are similar or not.

(a) We see that in triangles ABC and PQR, we have

m∠A = m∠P = 41°,   m∠B = m∠Q = 85° and m∠C = m∠R = 54°.

So, ΔABC and ΔPQR are similar by AA similarity statement.

(b) We see that in triangles ABC and DEF, we have

AB = 4, BC = 5, CA = 3, DE = 24, EF = 30 and FD = 18.

So, we have

$\dfrac{DE}{AB}=\dfrac{EF}{BC}=\dfrac{FD}{CA}=6.$

That is, the corresponding sides of two triangles are proportional.

Thus, ΔABC and ΔDEF are similar by proportionality statement.