Geometry - Pythagoras Theorem Review

Transformations Geometry

Multiple Choice

What transformation is shown?

• Reflection

• Rotation

• Translation

Multiple Choice

Name the transformation.

• Translation
• Reflection
• Rotation

Multiple Choice

The original figure prior to a transformation.

• Pre-image
• Image

Multiple Choice

The result of a transformation.

• Pre-image
• Image

Multiple Choice

Identify the transformation from ABC to A'B'C'.

• 90^o clockwise rotation
• 90^o counter clockwise rotation
• Reflection across the y-axis
• Reflection across the x-axis

Multiple Choice

How is triangle ABC being translated to triangle A'B'C'?

• up 3, left 8
• up 9, left 4
• down 3, right 8
• down 9, right 4

Multiple Choice

Write a rule for the translation.

• (x -1, y + 2)

• (x -2, y + 1)

• (x +2, y - 1)

• (x +1, y - 2)

Multiple Choice

Name the series of transformations that maps ABC onto DEF

• reflect over x then translate left 6 up 1
• reflect over y then translate down 6 left 1
• translate right 6 down 1, then reflect over x
• rotate 90 clockwise then reflect over y

Multiple Choice

Identify the transformation from A to D.

• 90^o Clockwise Rotation
• 180^o Rotation
• 270^o Clockwise Rotation
• 360^o Rotation

Multiple Choice

Triangle A is rotated 270° clockwise with the origin as the center of rotation to create a new figure. Which triangle shows the new location?

• A

• B

• C

• D

Multiple Choice

If you were to rotate ABCD 90° counterclockwise about the origin, what would the coordinate of A' be?

• (-5, 5)
• (-3, 5)
• (-5, 3)
• (-3, 3)

Triangle Sum Theorem

• states that the three interior angles of any triangle add up to 180 degrees

Multiple Choice

What is the measure of the missing angle, D?

• 49
• 59

• 90

• 41

Pythagoras' Theorem

Identifying the Hypotenuse

Opposite 90 degrees and always the longest side 

Multiple Choice

Which side p,q,r is the hypotenuse

• p

• q

• r

Sides

• q and r are shorter than the hypotenuse

• they are also known as the 'legs'

Finding the hypotenuse

Finding a missing 'leg'

Multiple Choice

Find x.

• 35
• 20
• 8
• 12

Multiple Choice

A ladder 20 m long rests against a vertical wall. If the foot of the ladder is 12 m away from the base of the wall, the height of the point on the wall where the top of the ladder reaches is :

• 8 m

• 10 m

• 16 m

• 32 m

Multiple Choice

If a man goes 15 m due north and then 8 m due east, then his distance from the starting point is :

• 7 m

• 17 m

• 23 m

• 120 m

Multiple Choice

Which of the following are NOT the lengths of sides of a right-angled triangles?

• 3 cm, 4 cm, 5 cm

• 6 cm, 8 cm, 10 cm

• 8 cm, 15 cm, 17 cm

• 9 cm, 12 cm, 18 cm

Multiple Choice

Which of the following is a right-angled

triangle?

Multiple Choice

• 5

• 6

• 10

• 11

Sometimes it is not always practical to find the length of sides of a right triangle using Pythagoras theorem

Therefore we need to learn some new mathematics to carry out our calculations when dealing with triangle sides and angles.

Name Sides in Right-Angled Triangles

• The Hypotenuse

• The opposite side

• The adjacent side

Multiple Choice

The hypotenuse is ...

• LM

• LN

• MN

Multiple Choice

The side opposite to angle

$$\theta$$  is ...

• LM

• LN

• MN

Multiple Choice

The side adjacent to angle

$$\theta$$  is ...

• LM

• LN

• MN

Multiple Choice

What is the length of the opposite side?

• 8

• 15

• 17

Multiple Choice

What is the length of the adjacent side?

• 8

• 15

• 17