master 8.24 extra practice 1 - ms. manery's class -...

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Extra Practice 1

Lesson 8.1: Parallel Lines 1. Which line segments are parallel? How do you know? a) b)

c) d)

2. Look at the diagram below. Find as many pairs of parallel line segments as you can.

3. Draw line segment EF of length 4 cm. Use what you know about parallel lines to draw square EFGH. How you can check you have drawn a square?

Master 8.24

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The right to reproduce or modify this page is restricted to purchasing schools. This page may have been modified from its original. Copyright © 2007 Pearson Education Canada

Extra Practice 2

Lesson 8.2: Perpendicular Lines 1. Which line segments are perpendicular? How do you know? a) b) d) e) 2. Draw line segment GK of length 7 cm. Mark a point S below GK.

Use any method to draw a perpendicular line through S. How do you know the line you drew is perpendicular to the line segment?

3. Draw line segment ST of length 5 cm. Use what you know about perpendicular lines to draw square STUV. How you can check you have drawn a square?

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Extra Practice 3

Lesson 8.3: Constructing Perpendicular Bisectors 1. Draw any line segment MN. Use a ruler to draw the perpendicular bisector.

How do you know you have drawn the perpendicular bisector of MN? 2. Draw a large obtuse ΔPQR.

Construct the perpendicular bisector of each side of the triangle. Label point T where the bisectors meet. Draw the circle with centre T and radius TP.

3. Draw a large circle.

Label its centre O. Draw quadrilateral ABCD with vertices on the circle. Construct the perpendicular bisector of each side of the quadrilateral. What do you notice about the perpendicular bisectors?

4. Draw line segment PR of length 5 cm.

Use what you know about perpendicular bisectors to construct square PSRT. How can you check you have drawn a square?

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Extra Practice 4

Lesson 8.4: Constructing Angle Bisectors 1. Draw obtuse ∠BCD = 176°. a) How many different methods can you use to bisect the angle? b) Describe each method.

Check that the bisector you drew using each method is correct. 2. Draw any obtuse ∠ABC.

Use a ruler and a compass to bisect the angle. Measure the two parts of the angle. Are they equal?

3. Draw a large ΔABC.

Construct the bisector of each angle. What do you notice?

4. Draw rhombus BCDE. Construct the bisector of each angle. What do you notice?

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Extra Practice 5

Lesson 8.5: Graphing on a Coordinate Grid 1. Write the coordinates of each point from A to H.

A _______________

B _______________

C _______________

D _______________

E _______________

F _______________

G _______________

H _______________

2. For each point in question 1, name the quadrant or axis that contains the point.

3. What can be said about the coordinates of point P in each case? a) P is in Quadrant 2. b) P lies on the x-axis. c) P is in Quadrant 4. d) P lies on the y-axis. e) P is at the origin. f) P is in Quadrant 3.

4. a) Plot these points on a coordinate grid: K(–3, 4), A(4, 4), T(3, 2), E(–2, 2). b) Join the points. Which shape is formed?

5. a) Plot these points on a coordinate grid: A(3, 5), B(–4, 5), C(–4, 2). b) Find the coordinates of point D that forms rectangle ABCD.

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Extra Practice 6

Lesson 8.6: Graphing Translations and Reflections 1. Trapezoid ABCD has vertices A(–1, –1), B(1, –1), C(1, 3), and D(–1, 1).

After a translation, the image of ABCD is A’(4, –3), B’(6, –3), C’(6, 1), D’(4, –1). a) Draw ABCD and A’B’C’D’ on a grid. b) Describe the translation.

2. Identify each transformation. a) b)

3. Plot these points on a coordinate grid: A(1, 6), B(2, 4), C(4, 4), O(0, 0)

a) Draw the image of quadrilateral ABCO after a translation 2 units left and 3 units up.

b) Draw its image after a reflection in the x-axis. c) Draw its image after a reflection in the y-axis. d) Draw its image after a reflection in the line through (0, 0) and (10, 10).

4. Plot these points on a coordinate grid: A(2, 1), B(–1, 2), C(1, 5). a) Translate each point 3 units left and 4 units down to get

image points A’, B’, C’. b) Write the coordinates of each point and its translation image.

What pattern do you see in the coordinates?

5. Plot the points in question 4. a) Reflect each point in the x-axis to get image points A’, B’, C’.

b) Write the coordinates of each point and its reflection image. What pattern do you see in the coordinates?

6. Plot the points in question 4. a) Reflect each point in the y-axis to get image points A’, B’, C’.

b) Write the coordinates of each point and its reflection image. What pattern do you see in the coordinates?

7. Plot the points in question 4. a) Reflect each point in the line through (–10, –10) and (10, 10)

to get image points A’, B’, C’. b) Write the coordinates of each point and its reflection image.

What pattern do you see in the coordinates?

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Extra Practice 7

Lesson 8.7: Graphing Rotations 1. a) Which clockwise rotation is the same as a 90° counterclockwise rotation?

b) Which clockwise rotation is the same as a 270° counterclockwise rotation? c) Which clockwise rotation is the same as a 60° counterclockwise rotation? d) Why do we do not need to include “clockwise” and “counterclockwise” when

describing a 180° rotation? 2. In each diagram, ΔF’G’H’ is the image of ΔFGH after a rotation about the origin.

Identify each rotation. a) b) c)

3. Plot these points on a coordinate grid: A(2, 1), B(–1, 2), C(1, 5)

a) Rotate each point +90° about the origin to get image points A’, B’, C’. b) Write the coordinates of each point and its rotation image.

What patterns do you see in the coordinates?

4. Plot the points in question 3. a) Rotate each point +180° about the origin to get image points A’, B’, C’. b) Write the coordinates of each point and its rotation image.


5. Plot the points in question 3. a) Rotate each point +270° about the origin to get image points A’, B’, C’. b) Write the coordinates of each point and its rotation image.


6. Plot the points M(–2, 4), N(–5, 0), P(–4, –2), and Q(–1, –1) on a coordinate grid. Join the points to form quadrilateral MNPQ. a) Reflect the quadrilateral in the x-axis. Then reflect the image in the y-axis. b) Which rotation is equivalent to a reflection in the x-axis followed by a reflection

in the y-axis?

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Extra Practice Sample Answers

Extra Practice 1 – Master 8.24 Lesson 8.1 1. Parts a and d; the lines never meet. 2. AD, FI, NH, and BC; KE, DF, JM, and NB; AB, NG, and DC; AI and FC

3. I use a ruler and a protractor to draw line segment GH parallel and equal to EF and 4 cm apart.

Extra Practice 2 – Master 8.25 Lesson 8.2 1. Parts b and c; the lines intersect at right angles. 2. I used a Mira. The lines intersect at right angles. 3. I use a protractor and a ruler to draw line segments VS and UT perpendicular to ST through points S and T.

VS = UT = ST = UV = 5 cm Extra Practice 3 – Master 8.26 Lesson 8.3 1. PQ divides line segment MN in two equal parts; line segments MN and PQ intersect at 90°.

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2.

3. Each perpendicular bisector passes through the centre of the circle.

4. In a square, the diagonals are equal and they bisect each other at right angles.

PR is one of the diagonals of square PSRT. I drew the perpendicular bisector of PR using the ruler and compass method.

Then I measured 2.5 cm above and below line segment PR and marked points S and T on the perpendicular bisector.

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Extra Practice 4 – Master 8.27 Lesson 8.4 1. a) I use a Mira; paper folding; the ruler and compass and the right triangle methods are more difficult to use

because of the angle measure.

b) I fold the paper so that BC lies along DC. The fold line is the angle bisector.

Or: I place the Mira so that the reflection of BC lies along DC. 2. Yes, the angles are equal.

3. The angle bisectors meet at one point. 4. In a rhombus, the diagonals bisect angles in each vertex of the rhombus.

Extra Practice 5 – Master 8.28 Lesson 8.5 1. A(2, 4), B(0, –3), C(3, –2), D(–1, 0), E(–4, –4), F(–3, 2), G(5, 0), H(0, 0) 2. A: Quadrant 1

B: y-axis C : Quadrant 4 D : x-axis E : Quadrant 3 F : Quadrant 2 G : x-axis H : both x- and y-axes

3. a) Its x-coordinate is negative and its y-coordinate is positive. b) Its y-coordinate is 0. c) Its x-coordinate is positive and its y-coordinate is negative. d) Its x-coordinate is 0. e) Both its x- and y-coordinates are 0. f) Both its x- and y-coordinates are negative.

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4. a)

b) Trapezoid

5. a)

b) D(3, 2)

Extra Practice 6 – Master 8.29 Lesson 8.6 1. a)

b) Translation 5 units right and 2 units down 2. a) Reflection in the y-axis b) Reflection in the x-axis

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3. a), b)

c), d)

4. a)

b) A(2, 1) →A’(–1, –3)

B(–1, 2) →B’(–4, –2) C(1, 5) →C’(–2, 1) The x-coordinates decrease by 3, the y-coordinates decrease by 4.

5. a)

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b) A(2, 1) →A’(2, –1) B(–1, 2) →B’(–1, –2) C(1, 5) →C’(1, –5) The x-coordinates are unchanged; the sign of the y-coordinates changes.

6. a)

b) A(2, 1) →A’(–2, 1)

B(–1, 2) →B’(1, 2) C(1, 5) →C’(–1, 5) The sign of the x-coordinates changes; the y-coordinates are unchanged.

7. a)

b) A(2, 1) →A’(1, 2)

B(–1, 2) →B’(2, –1) C(1, 5) →C’(5, 1) The x- and y-coordinates are interchanged.

Extra Practice 7 – Master 8.30 Lesson 8.7 1. a) 270° b) 90° c) 300°

d) Rotations are equivalent. 2. a) 180° about the origin b) 90° about the origin c) –90° about the origin

3. a)

b) A(2, 1) →A’(–1, 2) B(–1, 2) →B’(–2, –1) C(1, 5) →C’(–5, 1) The x- and y-coordinates are interchanged. Then the x-coordinates change sign.

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4. a)

b) A(2, 1) →A’(–2, –1) B(–1, 2) →B’(1, –2) C(1, 5) →C’(–1, –5) The x- and y-coordinates change signs.

5. a)

b) A(2, 1) →A’(1, –2) B(–1, 2) →B’(2, –1) C(1, 5) →C’(5, –1) The original coordinates are interchanged. Then the y-coordinates change signs.

6. a)

Point After a

reflection in the x-axis

After a reflectionin the y-axis

M(−2, 4) M′(−2, −4) M′′(2, –4)

N(−5, 0) N′(−5, 0) N′′(5, 0)

P(−4, −2) P′(−4, 2) P′′(4, 2)

Q(−1, −1) Q′(−1, 1) Q′′(1, 1) b) Rotation of 180°

master 8.24 extra practice 1 - ms. manery's class -...

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