Similar Triangles: Identifying and defining elements

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?

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Video Solution

Step-by-Step Solution

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

B=E=40 B=E=40

C=F=60 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?

AAABBBCCCDDDEEEFFF

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 following two triangles:

AAABBBCCCDDDEEEFFFAngles 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 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 FD

Exercise #4

Look at the two triangles below:

AAABBBCCCDDDEEEFFF

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 E

Exercise #5

Look at the two triangles below:

AAABBBCCCDDDEEEFFF

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 F

Exercise #6

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

No

Exercise #7

Are the below triangles similar?

AAABBBCCCDDDEEEFFF

Video Solution

Step-by-Step Solution

Use the similarity theorems.

Answer

Yes

Exercise #8

Are the triangles below similar?

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Video Solution

Step-by-Step Solution

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

Answer

No

Exercise #9

Look at the parallelogram ABCD below.

AAABBBDDDCCC

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 #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?

AAABBBCCCDDDEEEFFF

Video Solution

Answer

No

Exercise #11

Look at the following two triangles below:

AAABBBCCCDDDEEEFFF

Angles B and F are equal.

Angle C is equal to angle D.

Which side corresponds to AB?

Video Solution

Answer

EF EF

Exercise #12

Look at the two triangles below:

AAABBBCCCDDDEEEFFF

Angle B is equal to angle E.

Angle C is equal to angle F.

Which side corresponds to side AC?

Video Solution

Answer

DF DF

Exercise #13

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?

AAABBBCCCDDDEEEFFF

Video Solution

Answer

Yes

Exercise #14

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?

AAABBBCCCDDDEEEFFF

Video Solution

Answer

Yes

Exercise #15

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?

AAABBBCCCDDDEEEFFF

Video Solution

Answer

Yes

Exercise #16

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?

AAABBBCCCDDDEEEFFF

Video Solution

Answer

No

Exercise #17

Are the triangles below similar?

666222444121212444888AAABBBCCCDDDEEEFFF

Video Solution

Answer

Yes

Exercise #18

Are the triangles below similar?

888444666444222333AAABBBCCCDDDEEEFFF

Video Solution

Answer

Yes

Exercise #19

Are the triangles below similar?

333555444444333555AAABBBCCCDDDEEEFFF

Video Solution

Answer

Yes

Exercise #20

Are the triangles below similar?

555444444555444444AAABBBCCCDDDEEEFFF

Video Solution

Answer

Yes