Look at the parallelogram ABCD below. A A A B B B D D D C C C What can be said about triangles ACD and ABD?

They are equal in area and perimeter.

Similar Triangles: Identifying and defining elements

Applying the formula

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

Look at the two triangles below:

Angle B is equal to angle F.

Angle C is equal to angle D.

Which angle corresponds to angle A?

Question 4

Look at the two triangles below:

Angle B is equal to angle E.
Angle A is equal to angle D.

Which angle corresponds to angle C?

Question 5

Look at the following two triangles:

Angles B and D are equal.
Angles A and F are equal.

Which side corresponds to AB?

Examples with solutions for Similar Triangles: 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

Look at the two triangles below:

Angle B is equal to angle F.

Angle C is equal to angle D.

Which angle corresponds to angle A?

Video Solution

Step-by-Step Solution

We use the angle-angle theorem to simulate triangles.

Let's observe the data we already have:

Angles B and F are equal.

Angle C is equal to angle D.

Therefore, the remaining angles must also be equal: angles A and E.

Answer

$E$

Exercise #4

Look at the two triangles below:

Angle B is equal to angle E.
Angle A is equal to angle D.

Which angle corresponds to angle C?

Video Solution

Step-by-Step Solution

As we have two pairs of corresponding angles, we will use the angle-angle theorem for triangle similarity.

Now that we know all angles are equal to each other, we note that the remaining angle that is equal and corresponds to angle C is angle F.

Answer

$F$

Exercise #5

Look at the following two triangles:

Angles B and D are equal.
Angles A and F are equal.

Which side corresponds to AB?

Video Solution

Step-by-Step Solution

As we have two equal angles, we will use the angle-angle theorem to simulate triangles.

We will compare the vertices: $A=F,B=D$

According to the data it seems that:

Side AC corresponds to side EF.

Side BC corresponds to side DE.

Therefore, side AB corresponds to side FD.

Answer

$FD$

Question 1

Look at the parallelogram ABCD below.

What can be said about triangles ACD and ABD?

Question 2

Are similar triangles necessarily congruent?

Question 3

Are the below triangles similar?

Question 4

Are the triangles below similar?

Question 5

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?

Exercise #6

Look at the parallelogram ABCD below.

What can be said about triangles ACD and ABD?

Video Solution

Step-by-Step Solution

According to the side-angle-side theorem, the triangles are similar and coincide with each other:

AC = BD (Any pair of opposite sides of a parallelogram are equal)

Angle C is equal to angle B.

AB = CD (Any pair of opposite sides of the parallelogram are equal)

Therefore, all of the answers are correct.

Answer

All answers are correct.

Exercise #7

Are similar triangles necessarily congruent?

Video Solution

Step-by-Step Solution

There are similar triangles that are not necessarily congruent, so this statement is not correct.

Answer

Exercise #8

Are the below triangles similar?

Video Solution

Step-by-Step Solution

Use the similarity theorems.

Answer

Yes

Exercise #9

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 #10

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

Question 1

Look at the following two triangles below:

Angles B and F are equal.

Angle C is equal to angle D.

Which side corresponds to AB?

Question 2

Look at the two triangles below:

Angle B is equal to angle E.

Angle C is equal to angle F.

Which side corresponds to side AC?

Question 3

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 4

Are two congruent triangles necessarily similar?

Question 5

Are the triangles similar?

Exercise #11

Look at the following two triangles below:

Angles B and F are equal.

Angle C is equal to angle D.

Which side corresponds to AB?

Video Solution

Answer

$EF$

Exercise #12

Look at the two triangles below:

Angle B is equal to angle E.

Angle C is equal to angle F.

Which side corresponds to side AC?

Video Solution

Answer

$DF$

Exercise #13

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 #14

Are two congruent triangles necessarily similar?

Video Solution

Answer

Yes

Exercise #15

Are the triangles similar?

Video Solution

Answer

Yes

Question 1

$$ A_1B_1=A_2B_2 $$

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 $$ A_2B_2C_2 $$ ?

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 50°.

Angle C is equal to 45°.

Angle E is equal to 50°.

Angle D is equal to 85°.

Are the triangles below similar?

Question 4

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 5

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?

Exercise #16

$A_1B_1=A_2B_2$

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

Exercise #17

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?

Video Solution

Answer

Yes

Exercise #18

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

Exercise #19

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?

Video Solution

Answer

Yes

Exercise #20

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?