Similarity Theorems: Identifying and defining elements

Angle B is equal to 40°

Angle C is equal to 60°

Angle E is equal to 40°

Angle F is equal to 60°

Are the triangles similar?

Given that the data shows that there are two pairs with equal angles:

$B=E=40$

$C=F=60$

The triangles are similar according to the angle-angle theorem, therefore triangle ABC is similar to triangle DEF.

Yes

Angle B is equal to 70 degrees

Angle C is equal to 35 degrees

Angle E is equal to 70 degrees

Angle F is equal to 35 degrees

Are the triangles similar?

The triangles are similar according to the angle-angle theorem.

Having two pairs of equal angles is sufficient to conclude that the triangles are similar.

Yes

Are the triangles below similar?

The sides of the triangles are not equal and, therefore, the triangles are not similar.

No

Angle B is equal to 60°

Angle C is equal to 55°

Angle E is equal to 60°

Angle F is equal to 50°

Are these triangles similar?

No

Angle B is equal to 70°.

Angle C is equal to 35°.

Angle E is equal to 70°.

Angle F is equal to 45°.

Are the triangles below similar?

No

Look at the two triangles below.

$A_2B_2=A_1B_1$

$A_2C_2=A_1C_1$

Angle $A_1$ is equal to angle $A_2$.

Is triangle $A_1B_1C_1$ equal to triangle $A_2B_2C_2$?

Yes

$A_1B_1=A_2B_2$

Angle$A_1$ is equal to $A_2$.

$A_1C_1=A_2C_2$

Is the triangle $A_1B_1C_1$congruent with the triangle$A_2B_2C_2$?

Yes

Angle B is equal to 70°.

Angle C is equal to 35°.

Angle E is equal to 70°.

Angle D is equal to 75°.

Are the triangles below similar?

Yes

Angle B is equal to 50°.

Angle C is equal to 45°.

Angle E is equal to 50°.

Angle D is equal to 85°.

Are the triangles below similar?

Yes

Angle B is equal to 70 degrees.

Angle C is equal to 35 degrees.

Angle E is equal to 75 degrees.

Angle F is equal to 35 degrees.

Are the triangles below similar?

Yes

Are the triangles below similar?

Yes

Are triangles below similar?

No

Are the triangles similar?

Yes

Are the triangles below similar?

Yes

Are the triangles below similar?

Yes

Are the triangles below similar?

Yes

Are the triangles below similar?

Yes