Geometry review

### 1.1. Geometry review

**Lesson 1 page 174:** In the picture below

a) How many right angles are there? Name the vertex and side of each right angle

b) What is the midpoint of line segment AB? What is the midpoint of line segment ED?

c) Determine the midpoint of line segment AE and line segment MN (shading those midpoints on the figure).

**Solution guide:**

- Count the number of right angles in the figure and then read the names of the vertices and sides of the right angle.
- The midpoint of line segment AB is the midpoint of A; B and the distance from that point to point A; B is equal.
- Find the similarity with the midpoint of line segment ED; AE and MN.

a) The given figure has 7 right angles:

Angle of vertex A, side AM, AE

Angle of vertex M, side MB, MN

Angle of vertex M, side MA, MN

Angle of vertex N, side NM, ND

vertex angle N, side NM; NE

Angle of vertex E, side EN, EA

Angle of vertex C, side CB, CD

b) Midpoint of line segment AB is point M (because M lies between A; B and MA = MB).

Midpoint of line segment ED is point N (because N lies between E; D and NE = ND)

c) Midpoint of line segment AE is point I (Take I between A; E such that IA = IE)

Midpoint of line segment MN is point K (Take K between M and N such that KM = KN)

**Lesson 2 page 174:** Find the perimeter of a triangle whose sides are 35cm, 26cm, and 40cm.

__Solution guide:__

- The perimeter of a triangle is equal to the sum of the lengths of its 3 sides (in the same units).

*Solution*

Perimeter of the given triangle is:

35 + 26 + 40 = 101 (cm)

Answer: 101 cm.

**Lesson 3 page 174:** Find the perimeter of a rectangular piece of land with a length of 125m and a width of 68m.

__Solution guide:__

- The perimeter of the rectangle is equal to the sum of the length plus the width (in the same units) and then multiplied by 2.

*Solution*

Perimeter of rectangular land is:

(125 + 68) x 2 = 386 (m)

Answer: 386 m.

**Lesson 4 page 174:** A rectangle and a square have the same perimeter. Assume that a rectangle is 60m long and 40m wide. Calculate the length of the side of the square.

__Solution guide:__

- Find the perimeter of the square (which is the perimeter of the rectangle) by adding the length plus the width (in the same units) and multiplying by 2.
- The side of the square is equal to the perimeter of the square divided by 4.

*Solution*

Perimeter of the rectangle is:

(60 + 40) x 2 = 200 (m)

The side of the square is:

200 : 4 = 50 (m)

Answer: 50 m.

### 1.2. Geometry review (continued)

**Lesson 1 page 174:** How many square centimeters does each figure below have?

__Solution guide:__

- Count the number of squares in each picture.

*Solution :*

The area of figure A is 8cm .^{2}

The area of figure B is 10cm .^{2}

Area of shape C is 18cm^{2}

Area of figure D is 8cm^{2}

**Lesson 2 page 175:** A rectangle is 12cm long and 6cm wide. The square has sides of 9cm.

a) Calculate the perimeter of each figure. Compare the perimeters of the two figures

b) Calculate the area of each figure. Compare the area of the two figures.

__Solution guide:__

- The perimeter of the rectangle is equal to the length plus the width (in the same units) and then multiplied by 2.
- The perimeter of a square is equal to the length of one side times 4.
- Area of rectangle is length times width (same unit of measure)
- The area of a square is equal to the length of a side times itself.

a) Perimeter of the rectangle is :

(12 + 6) x 2 = 36 (cm)

Perimeter of the square is:

9 x 4 = 36 (cm)

Square and rectangle have equal perimeter.

b) Area of the rectangle:

12 x 6 = 72 (cm^{2})

Area square :

9 x 9 = 81 (cm^{2})

The area of the square is larger than the area of the rectangle:

81 – 72 = 9 (cm^{2})

**Lesson 3 page 175: **Find a way to calculate the area of a shape H with the following dimensions

__Solution guide:__

- Divide the given shape into smaller squares and rectangles and find the area of those shapes.
- The area of the figure to be found is equal to the sum of the areas of the subdivisions.

__Method 1:__ The given figure can be divided as follows:

The area of the large square is:

6 x 6 = 36 (cm^{2})

The area of the small square is:

3 x 3 = 9 (cm^{2})

The area of figure H is:

36 + 9 = 45 (cm^{2})

__Method 2:__ The given figure can be divided into the following shapes:

The area of the small rectangle is:

6 x 3 = 18 (cm^{2})

The area of the large rectangle is:

9 x 3 = 27 (cm^{2})

The area of figure H is:

18 + 27 = 45 (cm^{2})

Answer: 45 cm^{2}

**Lesson 4 page 175: **

Given 8 triangles, each shape as shown below:

Arrange it in the form below:

**Solution guide:**

- Divide the shape to be folded into the given triangles.

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