7 Geometry

7.01 Angles and triangles

7.02 Transformations and congruence

7.03 Testing for triangle congruence

7.04 Using triangle congruence

7.05 Quadrilaterals built from triangles

Level 8

7.01 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

VCMMG291

Define congruence of plane shapes using transformations and use transformations of congruent shapes to produce regular patterns in the plane including tessellations with and without the use of digital technology

VCMMG292

Develop the conditions for congruence of triangles

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