In Geometry we work with 2D shapes, angles and lines.

Construction of geometric figures

In this Lesson you will learn how to construct, or draw lines, work with different lines,

angles and shapes.

Bisecting lines

When we construct, or draw, geometric figures, we often need to bisect lines or angles.

Bisect means to cut something into two equal parts. There are different ways to bisect

a line segment.

BISECTING A LINE SEGMENT WITH A RULER

Follow the steps.

Step 1: Draw line segment AB, 12cm and find the middle = 6cm. (the midpoint)

Step 2: Draw any line segment through the midpoint.

CD bisects line AB at F and is called a bisector. It bisects AB and therefore AF = FB.

Step 1 Place the compass on one endpoint of the line segment (point A). Draw an arc above and below the line. (Notice that all the points on the arc above and below the line are the same distance from point A.)

Step 2 Without changing the compass width, place the compass on point B. Draw an arc above and below the line so that the arcs cross the first two. (The two points where the arcs cross are the same distance away from point A and from point B.)

Step 3 Use a ruler to join the points where the arcs intersect. This line segment (CD) is the bisector of AB.

Equilateral Triangle: An equilateral triangle is a triangle where all the sides and all the angles are equal.

An equilateral triangle is also called an acute triangle because all 3 angles = 60°

and all sides are equal.

Isosceles triangle:

An isosceles triangle is the one with two sides equal and two equal angles.

Scalene triangle:

In a scalene triangle, no sides and angles are equal to each other.

Right angled Triangle:

An right angled triangle is a triangle where one of the angles = 90 °

Complementary and Supplementary Angles:

Complementary angles always add up to 90 degrees. Supplementary

angles always add up to 180 degrees

DIFFERENT TYPES OF ANGLES

QUESTIONS

1. Name the following angles:

a. 180 degrees

b. 40 degrees

c. 360 degrees

d. 120 degrees

e. 90 degrees

2. Write down the complement of :

a. 35 degrees

b. 80 degrees

c. 72 degrees

3. Write down the supplement of:

a. 35 degrees

b. 80 degrees

c. 72 degrees

4. Write down ALL the properties of the triangles:

a. Isosceles

b. Scalene

c. Equilateral

d. Right angled

5. Write down the name of the following angles:

a. Greater than 90 but less than 180 degrees

b. 90 degrees

c. Less than 90 degrees

d. Angles around a point (360 degrees)

e. 180 degrees

f. Sum of the angles is 180 degrees

g. Sum of the angles is 90 degrees.

6. Match the correct letter with the correct number:

CORRECT ANSWERS

Identify and classify quadrilaterals

A quadrilateral is a plane figure that has four straight lines, joined together to form four verticals. A vertex is the

point at which two straight lines meet to form an angle. Quadrilaterals can be identified by the size of their angles or

the lengths of their sides.

Important Terms:

Quadrilateral: A plane figure that has four straight lines, join together to form four vertices (corners).

Vertex: The point at which two straight lines meet to form an angle.

Adjacent sides: Two lines/sodes that meetat a vertex of the polygon.

Things to remember:

Note: The sum of the interior angles of rectangles and squares are 360°

AB is the same length as DC (AB = DC)

AB is parallel to DC (AB ‖ DC)

AD is the same length as BC (AD = BC)

AD is parallel to BC (AD ‖ BC)

AE is the same length as EC (AE = EC)

DE is the same length as EB (DE = EC)

The interior angle of A is the same as the Interior angle of C ( = )

The interior angle of B is the same as the Interior angle of D ( = )

Triangle ABE or ΔABE is the same as ΔCDE ( ΔABE ΔCDE )

Rotate AND

And ΔADE is the same as ΔCBE ( ΔADE ΔCBE )

Construct quadrilaterals:

All the angles in squares and rectangles are 90°. You can construct a square if you have the measurements of one

side because all the sides are the same length. To construct a rectangle, you need its length and breadth/width

measurements.

Construct quadrilaterals AB, BC, CD & DA = 45mm. All 4 corners are 90°

Your quadrilateral will look similar to this.

(Remember to right the measurements on the sides)

Construct a parallelogram:

Construct quadrilaterals ABCD with AB = 40mm, BC = 25mm, CD = 40mm, AD = 25mm and = 120°

Your quadrilateral will look similar to this.

(Remember to right the measurements on the sides)

The last instruction shows how to construct a corresponding angle at  to . The result in a line that is parallel to

DC. We could have constructed a co-interior angle of 60° to at Â.

Exercise 1:

1. You need the above construction of a parallelogram for this question.

Measure Â, and Ĉ. What do you notice?

2. Construct each quadrilateral. Use the information on each sketch.

a) b) c)

3. Construct each parallelogram.

a) Length = 55mm, Width = 40mm & acute angle 50°

b) Length = 60mm, Width = 35mm & obtuse angle 140°

Properties of Quadrilaterals:

Exercise 2:

1. Six quadrilaterals are described below. Identify each on.

a) All angles in this special type of rhombus are 90° and all sides are the same length.

b) Two pairs of adjacent sides and one pair of opposite angles are equal.

c) The opposite angles are equal and the opposite sides are both equal and parallel.

d) The opposite angles are equal. The sides are all the same length.

e) Two pairs of opposite sides are equal and parallel. All angles are the same size.

f) The four sides can all be different lengths. One pair of opposite sides is parallel.

2. Calculate the sizes of the unknown angles. Show calculations.

a) b) c)

Homework 20 & 21 August:

Please do this work in your books. Exercises and pages are marked out below.

We will go through this when you return to school.

• Exercise 11.3 – Page 111

• Exercise 11.4 – Page 112

• Exercise 11.5 – Page 114

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -