8 Geometry

8.01 Angles and triangles

8.02 Transformations and congruence

8.03 Testing for triangle congruence

8.04 Using triangle congruence

8.05 Quadrilaterals built from triangles

Stage 4

8.01 Angles and triangles

Worksheet

Angles

1

State whether the angles in each diagram below are supplementary:

a

b

c

d

2

State whether the angles in each diagram below are complementary:

a

b

c

d

3

State whether the following pairs of angles are either complementary or supplementary:

a

90\degree & 90\degree

b

88\degree & 2\degree

c

47\degree & 133\degree

d

36\degree & 54\degree

e

25\degree & 155\degree

f

62\degree & 28\degree

g

78\degree & 102\degree

h

177\degree & 3\degree

4

How many degrees in a revolution?

Unknown angles

5

Given that the angles in the diagrams below are supplementary, find the value of x:

a

b

c

d

e

f

g

h

6

Given that the angles in the diagram below are complementary, find the value of x:

a

b

c

d

7

Find the value of the pronumerals in each of the following diagrams:

a

b

c

d

e

f

g

h

Angle sum of a triangle

8

Find the value of x in the following diagrams:

a

b

c

d

e

f

g

h

i

9

Consider the given triangle:

a

Find the value of x.

b

Using the angles, classify the triangle.

10

Consider the given triangle:

a

Find the value of x.

b

Hence, find the size of \angle ACB.

11

Consider the given diagram:

a

Find the value of x.

b

Find the value of y.

Properties of triangles

12

State whether it is possible to form a triangle given the following side lengths:

a

6, 3, and 8

b

3, 5, and 9

c

9, 6, and 6

d

13, 7, and 6

e

10, 20, and 9

f

14, 18, and 13

13

Consider the given triangle:

a

Find the sum of the interior angles in the triangle.

b

Is the largest angle opposite the shortest, medium or longest side?

c

Is the smallest angle opposite the shortest, medium or longest side?

14

Consider the given triangle:

State the longest side of this triangle.

15

Consider the given triangle:

State the largest angle of this triangle.

16

Consider the given triangle:

State the shortest side of the triangle.

17

Consider the given triangle:

State the smallest angle of the triangle.

18

Consider the given triangle:

Write down the sides of the triangle from smallest to largest.

19

Consider the given triangle:

a

Find the value of x.

b

Find the size of \angle CAB.

c

Find the size of \angle ABC.

d

Find the size of \angle BCA.

e

Hence, state which side is the longest side of the triangle.

20

Consider the figure shown:

a

State what type of triangle the outer triangle is.

b

Find the value of a.

c

Find the value of b.

21

Consider the figure shown:

a

Find the value of a.

b

Hence, find the value of b.

22

Consider the figure shown:

a

Find the value of x.

b

Hence, find the value of m.

Outcomes

MA4-17MG

classifies, describes and uses the properties of triangles and quadrilaterals, and determines congruent triangles to find unknown side lengths and angles

MA4-18MG

identifies and uses angle relationships, including those related to transversals on sets of parallel lines

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