Similarity Theorems: Identifying and defining elements

Question 1

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?

Question 2

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?

Question 3

Are the triangles below similar?

Question 4

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?

Question 5

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?

Examples with solutions for Similarity Theorems: Identifying and defining elements

Exercise #1

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?

Video Solution

Step-by-Step Solution

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.

Answer

Yes

Exercise #2

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?

Video Solution

Step-by-Step Solution

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.

Answer

Yes

Exercise #3

Are the triangles below similar?

Video Solution

Step-by-Step Solution

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

Answer

Exercise #4

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?

Video Solution

Answer

Exercise #5

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?

Video Solution

Answer

Yes

Question 1

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?

Question 2

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?

Question 3

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?

Question 4

Are the triangles below similar?

Answer

Exercise #9

Are the triangles below similar?

Video Solution

Answer

Yes

Exercise #10

Are the triangles below similar?

Video Solution

Answer

Yes

Question 1

Are the triangles below similar?

Question 2

Are the triangles below similar?

Question 3

Are the triangles below similar?

Question 4

Are the triangles similar?

Answer

Question 1

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 $$ A_2B_2C_2 $$ ?

Question 2

$$ A_1B_1=A_2B_2 $$

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 $$ A_2B_2C_2 $$ ?

Exercise #16

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 $A_2B_2C_2$ ?

Video Solution

Answer

Yes

Exercise #17

$A_1B_1=A_2B_2$

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 $A_2B_2C_2$ ?

Video Solution

Answer

Yes