Geometric Figures Lesson

Unit 3- Geometric Figures - Angle & Line Relationships

By Brandy Stapleton

Angle Relationships

We have talked about the following angle Relationships.

​

Vertical Angles

Linear Pair

Adjacent Angles

Complimentary

Supplementary​

​

Multiple Select

Which angles are a VERTICAL pair?

• <AXB & <EXD

• <CXF & <GXE

• <FXD & <AXG

• <BXC & <BXE

• <AXG & <BXC

Multiple Select

Which angles are a LINEAR pair?

• <AXB & <EXD

• <CXF & <FXD

• <FXD & <AXG

• <BXC & <BXE

• <AXG & <GXD

Angle Relationships

We have talked about the following angle Relationships.

​

Vertical Angles

Linear Pair

Adjacent Angles

Complimentary

Supplementary​

​

Multiple Select

Which angles are ADJACENT?

• <AXB & <EXD

• <CXF & <FXD

• <FXD & <AXG

• <BXC & <GXB

• <AXG & <GXF

Fill in the Blanks

Identify and angle that is

COMPLIMENTARY

with <CXF ...

<

(use only three letters in your answer

Fill in the Blanks

Identify and angle that is

SUPPLEMENTARY

with <GXB ...

<

(use only three letters in your answer

the Math of it...

​We use the angle relationships to CREATE equations and solve for unknowns.

Questions to guide you...

1. What is the angle relationship?

2. And this means the angles are... ​

   1. vertical angles are congruent

   2. complimentary add to 90 degrees

   3. supplementary add to 180 degrees​ ***adjacent add to another angle sum​

Multiple Choice

What is the value of x?

• 60
• 26
• 14
• 10

Multiple Choice

Are these angles an example of complementary, supplementary, or neither?

• Complementary
• Supplementary
• Neither

Multiple Choice

Find the value of x. 

• 17
• 28
• 68
• 39.5

Multiple Choice

Find the value of x. 

• 14
• 112
• 108
• 104

Multiple Choice

If ∠C and ∠D are a linear pair, and the measure of ∠D = 4x+5, and ∠C = 15x-15, what is the measure of ∠C?

• 135
• 45
• 125
• 90

Two adjacent angles add to the sum of the whole angle!

​

​Angle Addition

Multiple Choice

Solve for x

• x = 77
• x = 7.5
• x = 8
• x = 18

Multiple Choice

First, use the angle addition postulate to create an equation and solve for x.

Then, find m<HIW

• x = 11

  m<HIW = 110

• x = 10

  m<HIW = 33

• x = 10

  m<HIW = 132

• x = 11

  m<HIW = 35

Two adjacent angles add to the sum of the whole angle!

​

​Segment Addition

Fill in the Blanks

EF=8x+20, FG=50, EG=150

What is x?

Fill in the Blanks

M is the midpoint of segment AB.

If AM = 6x-15 and MB = 105,

what is x?

​TRIANGLE RELATIONSHIPS

Multiple Choice

The Triangle Sum Theorem states that the sum of all angles in a triangle is ______. 

• 45°
• 90°
• 180°
• 360°

Multiple Choice

Determine the missing angle.

• 47
• 57
• 53
• 133

Multiple Choice

Determine the missing angle.

• 145
• 55
• 35
• 45

We've talked about these:

• angle bisector

• perpendicular bisector

• median

• altitude​

​

​Special Line Segments

Multiple Choice

The figure is an example of a(n) ...

• altitude 
• perpendicular bisector
• midsegment
• angle bisector

Multiple Choice

The figure is an example of a(n) ...

• angle bisector
• perpendicular bisector
• median
• midsegment

Multiple Choice

Given 
∠BAN ≅ ∠NAC
BR = RC.
Segment AT is a(n)....

• Perpendicular Bisector
• Altitude
• Angle Bisector
• Median

Multiple Choice

Given 
∠BAN ≅ ∠NAC
BR = RC.
Segment AR is a(n)....

• Perpendicular Bisector
• Altitude
• Angle Bisector
• Median

Multiple Choice

We haven't talked about this one yet, but it connects the midpoints of two sides of a triangle...

The figure is an example of a(n) ...

(See if you can guess it)

• median
• altitude
• midsegment
• angle bisector

​Isosceles & Equilateral Triangles

​Isosceles Triangles have two congruent base angles and the side opposite those are congruent.

​

In an Equilateral Triangle, all three angles are congruent (60 degrees) and all three sides are congruent.​

Multiple Choice

What is the length of DC

• 4
• 1
• 2
• 3

Multiple Choice

What is the measure of ∠S?

• 60⁰

• 52⁰

• 45⁰

• 36⁰

Multiple Choice

What is the measure of ∠A?

• 46

• 134

• 90

• 88

Multiple Choice

What is the value of x?

• 16

• 60

• 8

• not enough information

Multiple Choice

Find x

• 3
• 4
• 2
• 10