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

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.

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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...

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

ColinJacobus ColinJacobus · Answer 2 · 2019-05-27T06:22:53+02:00

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

[tex]\dfrac{DE}{AB}=\dfrac{EF}{BC}=\dfrac{FD}{CA}=6.[/tex]

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

Thus, ΔABC and ΔDEF are similar by proportionality statement.