Question

In triangle ABC, angle A is 35º and angle B is 20°. Select all triangles which are similar totriangle ABC

Answer 1

To check the simliarity of two triangles only using angles, we can use the correspnding angles criterion. If two pairs of correspondent angles are equal, both triangles are similar.

If two pairs corresponding angles are equal, then the third pair of corresponding angles is equal too.

Just to keep in mind, the sum of the three angles if a triangle is always 180. Then, for trangle ABC, if angle A is 35 and angle B is 20, then, angle C is:

`\begin{gathered} A+B+C=180^o^{} \\ C=180^o-35^o-20^o \\ C=125^o \end{gathered}`

Angle C is 125°.

Let's check each triangle:

A. Triangel DEF where D is 35° and E is 20° is similar, since corresponding pairs of angles A-D and B-E are congruent.

B. Triangle GHI where G = 35° and I = 30° is NOT similar, since corresponding pair of angles I-C are not congruent (30 and 125). No angle in triangle ABC is 30°.

C. Triangle JKL where J is 35° and L is 125° is similar, corresponding pairs of angles A-J and C-L are congruent (35° and 125°).

D. Triangle MNO with N = 20° and O = 125° is similar, since pairs of corresponding angles B-N and C-O are congruent (20° and 125°)

E. Triangle PQR with Q = 20° and R = 30° is NOT similar, since pair of corre