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?

AAABBBCCCDDDEEEFFF

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?

AAABBBCCCDDDEEEFFF

Question 3

Are the triangles below similar?

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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?

AAABBBCCCDDDEEEFFF

Question 5

Are triangles below similar?

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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?

AAABBBCCCDDDEEEFFF

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

Are the triangles below similar?

666999888555999888AAABBBCCCDDDEEEFFF

Video Solution

Step-by-Step Solution

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

Answer

No

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?

AAABBBCCCDDDEEEFFF

Video Solution

Answer

No

Exercise #5

Are triangles below similar?

777555444777555333AAABBBCCCDDDEEEFFF

Video Solution

Answer

No

Question 1

Are the triangles below similar?

666222444333111222AAABBBCCCDDDEEEFFF

Question 2

Are the triangles below similar?

555444444555444444AAABBBCCCDDDEEEFFF

Question 3

Are the triangles below similar?

666222444121212444888AAABBBCCCDDDEEEFFF

Question 4

Are the triangles below similar?

333555444444333555AAABBBCCCDDDEEEFFF

Question 5

Are the triangles below similar?

888444666444222333AAABBBCCCDDDEEEFFF

Exercise #6

Are the triangles below similar?

666222444333111222AAABBBCCCDDDEEEFFF

Video Solution

Answer

Yes

Exercise #7

Are the triangles below similar?

555444444555444444AAABBBCCCDDDEEEFFF

Video Solution

Answer

Yes

Exercise #8

Are the triangles below similar?

666222444121212444888AAABBBCCCDDDEEEFFF

Video Solution

Answer

Yes

Exercise #9

Are the triangles below similar?

333555444444333555AAABBBCCCDDDEEEFFF

Video Solution

Answer

Yes

Exercise #10

Are the triangles below similar?

888444666444222333AAABBBCCCDDDEEEFFF

Video Solution

Answer

Yes

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 \( A_2B_2C_2 \)?

A1A1A1B1B1B1C1C1C1A2A2A2B2B2B2C2C2C2

Question 2

Are the triangles similar?

AAABBBCCCDDDEEEFFF

Question 3

\( A_1B_1=A_2B_2 \)

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\( A_2B_2C_2 \)?

A2A2A2C2C2C2B2B2B2A1A1A1B1B1B1C1C1C1

Question 4

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

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?

AAABBBCCCDDDEEEFFF

Exercise #11

Look at the two triangles below.

A2B2=A1B1 A_2B_2=A_1B_1

A2C2=A1C1 A_2C_2=A_1C_1

Angle A1 A_1 is equal to angle A2 A_2 .

Is triangle A1B1C1 A_1B_1C_1 equal to triangle A2B2C2 A_2B_2C_2 ?

A1A1A1B1B1B1C1C1C1A2A2A2B2B2B2C2C2C2

Video Solution

Answer

Yes

Exercise #12

Are the triangles similar?

AAABBBCCCDDDEEEFFF

Video Solution

Answer

Yes

Exercise #13

A1B1=A2B2 A_1B_1=A_2B_2

AngleA1 A_1 is equal to A2 A_2 .

A1C1=A2C2 A_1C_1=A_2C_2

Is the triangle A1B1C1 A_1B_1C_1 congruent with the triangleA2B2C2 A_2B_2C_2 ?

A2A2A2C2C2C2B2B2B2A1A1A1B1B1B1C1C1C1

Video Solution

Answer

Yes

Exercise #14

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 #15

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

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?

AAABBBCCCDDDEEEFFF

Question 2

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

Exercise #16

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 #17

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