Math 7 Unit 3

Geometry and

Measurement

The area of a triangle is related to the area of a parallelogram with the same base and height.

True or False

The area of a triangle is related to the area of a parallelogram with the same base and height.

True

Angle bisectors can be constructed by using a compass and a ruler.

True or False

Angle bisectors can be constructed by using a compass and a ruler.

True

The drawing below shows a(n)

The drawing below shows a(n)

Angle Bisector

The drawing below shows a(n)

The drawing below shows a(n)

Perpendicular Bisector

The height of a parallelogram is always at right angles to its ____________________.

The height of a parallelogram is always at right angles to its ____________________.Base

What is the area of the triangle shown below? Round your answer to the nearest tenth of a square centimetre.

What is the area of the triangle shown below? Round your answer to the nearest tenth of a square centimeter.

Area of a triangle = b x h ÷ 2A = 14.7cm x12.9 cm ÷ 2A = 94.815

The area of the triangle is 94.8 cm .2

The measure of DEF is 84°. If the angle is bisected by line segment EG, what is the measure of the two resulting angles?

The measure of DEF is 84°. If the angle is bisected by line segment EG, what is the measure of the two resulting angles?

84 ÷ 2 = 42The two resulting angles would each be 42°.

A local sports team held a contest to choose the new team logo. All submitted entries had to use two parallelograms and one triangle with the dimensions given below. What would the total area be for the winning logo?

A local sports team held a contest to choose the new team logo. All submitted entries had to use two parallelograms and one triangle with the dimensions given below. What would the total area be for the winning logo?

Area of triangle = b x h ÷ 2A = 6 x 6 ÷ 2A = 18

Area of parallelogram = b x h A = 8 x 8A = 64

Total area of new logo = 1 triangle + 2 parallelograms A = 18 + (2 x 64) A = 146 The total area of the logo would be 146 cm .2

George is painting a triangular mural to cover one of his attic walls. How much area will George have to paint?

George is painting a triangular mural to cover one of his attic walls. How much area will George have to paint?

Area of a triangle = b x h ÷ 2A = (6.1 x 2) x 3.5 ÷ 2A = 12.2 x 3.5 ÷ 2 A = 21.35

The area of the wall is 21.35 m .2

What is being constructed in this diagram?

a. angle bisector c. parallel lineb. congruent line d. perpendicular bisector

What is being constructed in this diagram?

a. angle bisector c. parallel lineb. congruent line d. perpendicular bisector

What type(s) of lines are represented in this photo?

a. divergent c. parallel and perpendicularb. parallel d. perpendicular

What type(s) of lines are represented in this photo?

a. divergent c. parallel and perpendicularb. parallel d. perpendicular

What is being constructed in this diagram?

What is being constructed in this diagram?

Angle Bisector

A parallelogram and a rectangle have the same base and height measurements. What do you know about the areas of these two shapes?

a. The area of the parallelogram is greater than the area of the rectangle.b. The area of the rectangle is greater than the area of the parallelogram.c. The areas of the two shapes are the same.d. The areas of the two shapes are unrelated.

A parallelogram and a rectangle have the same base and height measurements. What do you know about the areas of these two shapes?

a. The area of the parallelogram is greater than the area of the rectangle.b. The area of the rectangle is greater than the area of the parallelogram.c. The areas of the two shapes are the same.d. The areas of the two shapes are unrelated.

Lines in the same plane that do not intersect are called ____________________ lines.

Lines in the same plane that do not intersect are called ____________________ lines.parallel

Afsha has enough paint to cover an area of 7.5 m2. She plans to paint a design on her bedroom wall in the shape of a parallelogram. If the design has a height of 2.5 m, what is the size of the base?

Afsha has enough paint to cover an area of 7.5 m2. She plans to paint a design on her bedroom wall in the shape of a parallelogram. If the design has a height of 2.5 m, what is the size of the base?

Area of a parallelogram = b x h 7.5 = b x 2.5 7.5 = 3 x 2.5

Therefore, the size of the base is 3 m.

Tia and her father are building a tree house in the shape of a triangle. How much wood will Tia need for the floor of her tree house?

Tia and her father are building a tree house in the shape of a triangle. How much wood will Tia need for the floor of her tree house?

Area of a Triangle = b x h ÷ 2A = 5 x 4.3 ÷ 2 A = 10.75

Tia will need 10.75 m of wood for the floor.2

Draw the perpendicular bisector of this line segment.

8 cm

Draw the perpendicular bisector of this line segment.

8 cm

Draw the angle bisector of this angle.

Draw the angle bisector of this angle.

What are two methods for drawing an angle bisector?

What are two methods for drawing an angle bisector?

1) using a compass and a ruler2) using a protractor and a ruler

What are three methods for drawing a perpendicular bisector?

What are three methods for drawing a perpendicular bisector?

The methods include using:· paper folding· a compass· a ruler and a right angle

Veronica has created a logo made up of her first initial. If she plans to sew the logo onto a banner, how much material does she need?

Veronica has created a logo made up of her first initial. If she plans to sew the logo onto a banner, how much material does she need?

Area of a parallelogram = b x hA = 4 x 40 A = 160 cm

Area of 2 parallelograms = 2 x 160A = 320 cm

She needs 320 cm of material.

2

2

2