Task Notes

Chapter 3 Test

CHAPTER 3

Chapter

Opener (slide 2)

Getting Ready

(slides 3 to 9)

Mid-Chapter

FAQ(slides 10

and 11)

ChapterFAQ

(slides 12 to 15)

Chapter 3Task

(slides 16 to 18)

Lessons3.1 – 3.3

(separate files)

Lessons3.4 – 3.6

(separate files)

Teaching Notes

Chapter Task BLM

Tech

Tip

Once you have classified a shape, you know a lot about it.

What shapes do you recognize here?What do you know about each shape?

Plane Geometry 3

BAnswer

1 Which equation matches this diagram?

A 180° – 60° = x

B x + 60° = 90°

C 360° – 60° = x

D x + 60° = 180°

Getting Ready

60°

x

3 Plane Geometry

AAnswer

2 Which equation matches this diagram?

A 70° + 25° + y = 180°

B 360° – 70° – 25° = y

C 25° + y = 70°

D 70° + 25° = y 25°y 70°

Getting Ready

3 Plane Geometry

BAnswer

3 What is the value of d ?

A 5°

B 85°

C 90°

D 105°85°

d

Getting Ready

3 Plane Geometry

CAnswer

4 What is the sum of the measures of theangles of a triangle?

A 60°

B 90°

C 180°

D 360°

Getting Ready

3 Plane Geometry

CAnswer

5 What is the value of x ?

A 55°

B 95°

C 125°

D 145°

125°

x

Getting Ready

3 Plane Geometry

FalseAnswer

6 Parallel lines intersect.

True

False

Getting Ready

3 Plane Geometry

DAnswer

7 Which shape is a quadrilateral?

A

B

C

D

Getting Ready

3 Plane Geometry

Method 1:Remember that supplementary angles sum to 180°. Find those angles that make up a straight line.

Look at line EC. ∠EBA and ∠ABC form a straight line. They will sum to 180° so

∠ABC = 180° – 35° = 145°. ∠CBD and ∠ABC form a straight line, so ∠CBD = 180° – ∠ABC ∠CBD = 180° – 145° = 35°.

So ∠DBE measures 135° because it forms a straight line when combined with ∠CBD.

35° B

E

A

C

D

Mid-Chapter FAQHow do I find the

missing angles if I am given intersecting lines?

Q

A

Reveal

3 Plane Geometry

Method 2:Remember that angles that are opposite to each other are equal.

∠CBD is opposite ∠EBA. This means that ∠EBA = 35° because the angles must be equal.

∠EBA and ∠ABC form a straight line. They will sum to 180° so

∠ABC = 180° – 35° = 145°.

∠ABC is opposite ∠EBD so they must be equal. ∠EBD is 145°.

35° B

E

A

C

D

How do I find the missing angles if I am given intersecting lines?

Mid-Chapter FAQQ

A

Reveal

3 Plane Geometry

Method 2:∠FGH and ∠GKM are corresponding angles, so they are equal. ∠GKM = 30°

∠GKM and ∠GKJ form a straight line. They sum to 180°.

∠GKJ = 180° – 30° = 150°

Reveal

30°

L

M

F

J

I

H

K

G

x

Given two parallel lines and a transversal, how can I determine an unknown angle?

Method 1:∠IGK is opposite ∠FGH, so they are equal. ∠IGK = 30°

∠IGK and ∠GKJ are interior angles on the same side of the transversal, so they sum to 180°.

∠GKJ = 180° – 30° = 150°

A1

A2

Chapter FAQ

Q

3 Plane Geometry

Reveal

3 Plane Geometry

If I have been given two of the interior angles of a triangle, how do I find the exterior angle of the triangle?

Method 1: The interior angles of a triangle sum to 180°. ∠CBD = 180° – 27° – 65° = 88°.∠CBD and ∠ABC form a straight line, so sum to 180°. ∠ABC = 180°– ∠CBD = 180° – 88° = 92°

Method 2: The sum of the two given angles equals the exterior angle required.

∠BCD + ∠CDB = 27° + 65° = 92°, so ∠ABC = 92°

27°

BA

C

D

x 65°

Chapter FAQ

A1

A2

Q

Reveal

Reveal

27°

B

A

C

D

65°

How do I find the missing angles of the quadrilateral?

Since AB and DC are parallel, the sum of ∠C and ∠B is 180°.

∠C = 180° – 27° = 153°.

The sum of the interior angles of a quadrilateral is 360°. Since I know three angles, I can subtract them from 360° to find ∠D.

∠D = 360° – 65° – 27° – 153° = 115°

Chapter FAQ

A

Q

Reveal

3 Plane Geometry

The sum of the interior angles of a polygon can be expressed as 180°(n – 2).

For a hexagon, 180°[(6) – 2] = 720°

Since the polygon is regular, all angles are equal. A hexagon has 6 sides, so divide 720° by 6 to get 120°.

If I am given a regular polygon, what would one of the interior angles measure?

Chapter FAQ

A

Q

Reveal

3 Plane Geometry

Chapter 3 TaskDesigning a Park

A town council has decided to build a local park. The park should be a fun place for people to visit, but also have a formal feel.Create a design for the park.

3 Plane Geometry

DESIGN CRITERIA

• Include parallel lines, transversals, and polygons in your design.

• Include angle measures, but only one angle should have been measured using a protractor.

Chapter 3 TaskDesigning a Park

3 Plane Geometry

REPORT CRITERIA

• Include a drawing of your design.

• Describe the features of the park and their benefits.

• Describe the angle relationships and other properties you used to determine the angle measures.

Chapter 3 TaskDesigning a Park

3 Plane Geometry