Question

Are the two triangles below similar?

A) Yes; they have congruent corresponding angles
B) No; they do not have congruent corresponding angles
C) Yes; they have proportional corresponding sides
D) No; they do not have proportional corresponding sides

Answer 1

Answer: Hello mate!

As we know, the sum of 3 internal angles of a triangle should add to 180°

So first, let's find the missing angles of both triangles:

triangle 1:

We have that one angle is equal to 27° and the other to 46°

then the missing angle is equal to 180° - 27° - 46° = 107°

triangle 2:

We have that one angle is 27° and the other is 108°, then the third angle is:

180° - 27° - 108° = 45°

Now, you can see that the triangles only have one angle in common (27°) and the other two are different, so the angles between them are not congruent corresponding.

Then the right answer is B: "No; they do not have congruent corresponding angles"

Answer 2

Answer:- B) No; they do not have congruent corresponding angles.

Explanation:-

In ΔGHI ,

∠G=46° and ∠I=27°

By angle sum property,

∠G+∠H+∠I=180°

⇒∠I=180°-∠G-∠H

⇒∠I=180°-46°-27°= 107°

In Δ JKL

∠K=108°and ∠L=27°

By angle sum property of triangles,

∠J+∠K+∠L=180°

⇒∠J=180°-∠L-∠K

⇒∠J=180°-27°-108°

⇒∠J=45°

Now we can see that there is only one pair of congruent angles [not two] in both the triangles i.e.∠I≅∠L.

⇒ They do not follow AA similarity criteria.

Thus ,the given triangles are not similar because they do not have congruent corresponding angles.