Establishing Triangle Similarity

Similar
Triangles

003: Engineering Principles

​Lesson Objectives

To be able to:

• Calculate missing angles of triangles

• Understand what a "similar triangle" is and what a "scale factor" is

• Calculate lengths of similar triangles
  

Basics of Triangles...

Types of Triangles

Multiple Choice

The triangle shown on the diagram is called

• Isosceles

• Right-angle

• Equilateral

• Scalene

Multiple Choice

The triangle shown on the diagram is called

• Isosceles

• Right-angle

• Equilateral

• Scalene

Multiple Choice

The triangle shown on the diagram is called

• Isosceles

• Right-angle

• Equilateral

• Scalene

Multiple Choice

The triangle shown on the diagram is called

• Isosceles

• Right-angle

• Equilateral

• Scalene

Multiple Choice

Angles in a triangle add up to

• 90°

• 180°

• 270°

• 360°

Multiple Select

Which of the following could be angles of a triangle?

[More than one correct answer]

• 90°, 30°, 60°

• 44°, 66°, 60°

• 27°, 29°, 124°

• 80°, 15°, 86°

• 78°, 24°, 78°

Simply subtract the two given angles from 180° as shown in the Practice Example →

​

​Calculating missing angles of triangles

Calculating missing angles of triangles...

Math Response

Calculate the missing angle of the triangle shown.

Type answer here

Correct Answer: 55

Deg^°

Rad

Math Response

Calculate the missing angle of the triangle shown.

Type answer here

Correct Answer: 35

Deg^°

Rad

Math Response

Calculate the missing angle of the triangle shown.

Type answer here

Correct Answer: 39

Deg^°

Rad

Math Response

Calculate the missing angle of the triangle shown.

Type answer here

Correct Answer: 66

Deg^°

Rad

Math Response

Calculate the missing angle of the triangle shown.

Type answer here

Correct Answer: 47

Deg^°

Rad

Math Response

Calculate the missing angle A of the triangle frame shown.

Type answer here

Correct Answer: 45

Deg^°

Rad

Math Response

Calculate the missing angle B of the triangle frame shown.

Type answer here

Correct Answer: 60

Deg^°

Rad

Math Response

Calculate the missing angle C of the triangle frame shown.

Type answer here

Correct Answer: 75

Deg^°

Rad

Math Response

Calculate the missing angle a of the triangle frame shown.

Type answer here

Correct Answer: 30

Deg^°

Rad

Math Response

Calculate the missing angle b of the triangle frame shown.

Type answer here

Correct Answer: 60

Deg^°

Rad

Math Response

Calculate the missing angle c of the triangle frame shown.

Type answer here

Correct Answer: 95

Deg^°

Rad

Math Response

Calculate the missing angle a of the triangle frame shown.

Type answer here

Correct Answer: 51

Deg^°

Rad

Math Response

Calculate the missing angle b of the triangle frame shown.

Type answer here

Correct Answer: 39

Deg^°

Rad

Math Response

Calculate the missing angle c of the triangle frame shown.

Type answer here

Correct Answer: 51

Deg^°

Rad

Math Response

Calculate the missing angle d of the triangle frame shown.

Type answer here

Correct Answer: 45

Deg^°

Rad

Two triangles are said to be similar if all 3 angles in both triangles are the same:

​

Calculating lengths of similar triangles

If two triangles are similar, then the lengths of one triangle can be calculated using the lengths of the other triangle by setting up a

​proportion of the large vs. the small triangle.

Calculating lengths of similar triangles

Calculating lengths of similar triangles...

Math Response

Two similar triangles are shown (ABC and DEF). Calculate the unknown length d of triangle DEF.

Type answer here

Correct Answer: 14

Deg^°

Rad

Math Response

Two similar triangles are shown (ABC and DEF). Calculate the unknown length e of triangle DEF.

Type answer here

Correct Answer: 12

Deg^°

Rad

Math Response

Two similar triangles are shown (ABC and DEF). Calculate the unknown length d of triangle DEF.

Type answer here

Correct Answer: 5.7

Deg^°

Rad

Math Response

Two similar triangles are shown (ABC and DEF). Calculate the unknown length e of triangle DEF.

(State the answer to one decimal place)

Type answer here

Correct Answer: 8.6

Deg^°

Rad

Math Response

Two similar triangles are shown (ABC and DEF). Calculate the unknown length e of triangle DEF.

Type answer here

Correct Answer: 10

Deg^°

Rad

Math Response

Two similar triangles are shown (ABC and DEF). Calculate the unknown length d of triangle DEF.

Type answer here

Correct Answer: 6.25

Deg^°

Rad

Math Response

Two similar triangles are shown (ABC and DEF). Calculate the unknown length d of triangle DEF.

Type answer here

Correct Answer: 9.6

Deg^°

Rad

Math Response

Two similar triangles are shown (ABC and DEF). Calculate the unknown length e of triangle DEF.

Type answer here

Correct Answer: 10

Deg^°

Rad

Math Response

Two similar triangles are shown (ABC and DEF). Calculate the unknown length d of triangle DEF.

Type answer here

Correct Answer: 8.5

Deg^°

Rad

Math Response

Two similar triangles are shown (ABC and DEF). Calculate the unknown length e of triangle DEF.

Type answer here

Correct Answer: 21.5

Deg^°

Rad

Math Response

Determine the missing length YZ for triangle XYZ.

Type answer here

Correct Answer: 9

Deg^°

Rad

Math Response

Determine the missing length XZ for triangle XYZ.

Type answer here

Correct Answer: 15

Deg^°

Rad

Math Response

Two similar triangles are shown (ABC and XYZ). Determine the missing length YZ for triangle XYZ.

Type answer here

Correct Answer: 7.5

Deg^°

Rad

Math Response

Two similar triangles are shown (ABC and XYZ). Determine the missing length XZ for triangle XYZ.

Type answer here

Correct Answer: 10

Deg^°

Rad

Math Response

Determine the unknown length BD for triangle ABD.

Type answer here

Correct Answer: 7.5

Deg^°

Rad

Math Response

Determine the unknown length AD for triangle ABD.

Type answer here

Correct Answer: 15

Deg^°

Rad

Math Response

Determine the unknown length AE for triangle ADE.

Type answer here

Correct Answer: 6.4

Deg^°

Rad

Math Response

Determine the unknown length AD for triangle ADE.

Type answer here

Correct Answer: 7.4

Deg^°

Rad

Math Response

Determine the unknown length CE for triangle CDE.

Type answer here

Correct Answer: 9.6

Deg^°

Rad

Math Response

Determine the unknown length BC for triangle ABC.

Type answer here

Correct Answer: 9

Deg^°

Rad

Poll

Select which lesson objectives you have achieved in this lesson:

• Calculate missing angles of triangles

• Understand what a "similar triangle" is and what a "proportion" is

• Calculate lengths of similar triangles

Recap - Lesson Objectives

To be able to:

• Calculate missing angles of triangles

• Understand what a "similar triangle" is and what a "scale factor" is

• Calculate lengths of similar triangles