### Key Concepts

- Learn to use protector, scale and compass.
- Draw a quadrilateral with given conditions
- Draw a figure to solve a problem
- Draw a figure using technology

**Geometric Shapes:**

Geometric shapes can be defined as a figure or area closed by a boundary which is created by combining the specific amount of curves, points, and lines.

The following are the different geometrical shapes.

Some geometrical shapes in real life:

### Let’s learn about angles:

An angle can be defined as the figure formed by two meeting at a common end point.

An angle is represented by the symbol ∠. Here, the angle below is ∠ABC.

The following illustration represents the different types of angles.

**Types of Angles**

**Quadrilateral:**

A quadrilateral is a polygon in Euclidean plane geometry with four edges and four vertices. Other names for quadrilateral include quadrangle and tetragon. A quadrilateral with vertices A, B, C and D.

### Properties of quadrilateral:

A quadrilateral has:

- Four sides (4 edges)
- Four vertices (4 corners)
- The sum of the interior angles is 360°.

Area: ½ x diagonal x (sum of perpendicular heights)

Perimeter: sum of sides of the quadrilateral

Draw a line segment of length 7.3 cm using a ruler.

**Solutions:**

Using a ruler, we can draw a line segment of length 7.3 cm as follows

**Step 1:** Mark a point A on the sheet

**Step 2:** Place 0 mark of the ruler at point A

**Step 3:** At 7.3 cm on the ruler, mark a point B on the sheet

**Step 4:** Now join A and B

**Using protractor:**

### Constructing Angles Using Protractor – Examples

**Example 1:**

Construct an acute angle of 60°.

**Step 1:**

Draw a line segment PA.

**Step 2:**

- Place the protractor on the line segment PA

- Place the midpoint of the protractor at point P, as shown in the figure.

**Step 3:**

- On PA from the right, start counting from 0° in the ascending order (counter-clockwise direction) and finally mark a point Q using a sharp pencil at the point showing 60° on the semi-circular edge of the protractor.

- Remove the protractor and join PQ.

- We get the required angle ∠APQ = 60°.

**8.2.1 Draw Geometric Figures or**** ****Draw a quadrilateral with given conditions**

- Construct a line segment of length 5.6 cm using a ruler and a compass.

**Solutions:**

RS = 5 cm

PS = 4 cm

∠S = 100°

∠R = 120°

For the construction of a quadrilateral with some of the measurements given, we first

draw a rough figure of the quadrilateral with the given dimensions, as shown below.

Now starting with the construction, the steps are:

**Step 1:** Draw a line segment of length 5 cm and mark the ends as S and R.

**Step 2:** Using a protractor, draw a line from point R making 120° and another line from point S making 100° with the line segment SR.

**Step 3:** Set your compass to the radius of 4 cm and make an arc from the point S on the 100° line. Mark the point as P where the arc intersects the line.

**Step 4:** Similarly, set the compass to the radius of 6 cm and make an arc from point R on the 120° line. Mark the point as Q where the arc intersects the line.

**Step 5:** Join the points P and Q.

You obtain the quadrilateral PQRS of the required measurements.

To construct an angle using a protractor, we must need the following mathematical instruments.

1. Ruler

2. Protractor

**8.2.2 Draw a figure to solve a problem**

- Mr Bearl coffee shop has desks shaped like equilateral triangles. He is planning to arrange a desk for 8 people. If two persons can sit at each edge of each desk, then make a sketch to show how many desks he needs.

He will need 6 desks to make the arrangement.

**8.2.3 Draw a figure using technology**

Mr Jason, who works as an architect in an engineering company, is supposed to draw a floor map. His manager gave him the value as follows:

One side of the floor should be 4 cm

The other side of the floor should be 5 cm

Two of the angles should be 60^{0}

**Solution:**

**Step 1:** Jason draws the first parallel line of 4 cm

**Step 2:** Jason then draws the first side by measuring 60^{0}

**Step 3:** Jason now duplicates each line segment to create pairs of parallel lines.

Advanced technology such as BIM, VR, and 3D printing is changing the field of architecture, from producing immersive visualization to streamlining communication. Architects are able to draw 3D pictures using computer technology.

## Exercise:

- If four sides and one diagonal of a quadrilateral are given:

Follow the following steps to draw the quadrilateral:

Construct a quadrilateral PQRS where PQ= 5 cm, QR = 7 cm, RS = 6 cm, PS = 6.5 cm and PR = 8 cm.

2. If two diagonals and three sides of a quadrilateral are given:

Follow the following steps to draw the quadrilateral:

Construct a quadrilateral ABCD, given that BC = 5.5 cm, AD = 6.5 cm, CD = 5 cm the diagonal AC = 6 cm and diagonal BD = 8 cm

3. If two adjacent sides and three angles of a quadrilateral are given:

Follow the following steps to draw the quadrilateral:

Construct a quadrilateral MIST where MI = 3.5 cm, IS = 6.5 cm, ∠M = 75°, ∠I = 105° and ∠S = 120°.

4. Write angles by looking at the pictures:

- Use your protractor to draw these angles:

(i) 40°

(ii) 125°

(iii) 25°

- Circle the alphabets with right angles.

- Fill in the blanks:

(i) A quadrilateral has …………… sides.

(ii) A quadrilateral has …………… angles.

(iii) A quadrilateral has …………… vertices, no three of which are……………… .

(iv) A quadrilateral has …………… diagonals.

(v) A diagonal of a quadrilateral is a line segment that joins two ……………… vertices

of the quadrilateral.

(vi) The sum of the angles of a quadrilateral is ……………… .

- The three angles of a quadrilateral are 76°, 54° and 108°. Find the measurement of the fourth angle.
- Draw line segments of the lengths given below:

(1) 5.3 cm (2) 6.7 cm (3) 3.8 cm

- Measure and write down the sizes of all the angles and the lengths of all the sides of each quadrilateral below.

Square

## What we have learnt:

- Learn to use protector, scale and compass.
- Draw a quadrilateral with given conditions
- Draw a figure to solve a problem
- Draw a figure using technology

### Concept Map:

#### Related topics

#### Addition and Multiplication Using Counters & Bar-Diagrams

Introduction: We can find the solution to the word problem by solving it. Here, in this topic, we can use 3 methods to find the solution. 1. Add using counters 2. Use factors to get the product 3. Write equations to find the unknown. Addition Equation: 8+8+8 =? Multiplication equation: 3×8=? Example 1: Andrew has […]

Read More >>#### Dilation: Definitions, Characteristics, and Similarities

Understanding Dilation A dilation is a transformation that produces an image that is of the same shape and different sizes. Dilation that creates a larger image is called enlargement. Describing Dilation Dilation of Scale Factor 2 The following figure undergoes a dilation with a scale factor of 2 giving an image A’ (2, 4), B’ […]

Read More >>#### How to Write and Interpret Numerical Expressions?

Write numerical expressions What is the Meaning of Numerical Expression? A numerical expression is a combination of numbers and integers using basic operations such as addition, subtraction, multiplication, or division. The word PEMDAS stands for: P → Parentheses E → Exponents M → Multiplication D → Division A → Addition S → Subtraction Some examples […]

Read More >>#### System of Linear Inequalities and Equations

Introduction: Systems of Linear Inequalities: A system of linear inequalities is a set of two or more linear inequalities in the same variables. The following example illustrates this, y < x + 2…………..Inequality 1 y ≥ 2x − 1…………Inequality 2 Solution of a System of Linear Inequalities: A solution of a system of linear inequalities […]

Read More >>
Comments: