Squares and Rectangles

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79 © M arshal l Ca vendish Int erna tional (Singapor e) Priv at e Limit ed.

Practice 1 Squares and Rectangles

Fill in the blanks with yes or no.

C

h

a

p

t

Is this a square? 1. Is this a rectangle?

2. Is this a square? 3. Is this a rectangle?

4. Is this a square? 5. Is this a rectangle?

Lesson 11.1 SquaresandRectangles

Squares and

Rectangles

Example

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Fill in the blanks.

Is this a square? Why or why not?

6.

Is this a rectangle? Why or why not?

7.

Is this a rectangle? Why or why not?

8.

Example

Yes

All its sides are of equal length,

and it has four right angles.

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Find the lengths of the unknown sides.

ABCD is a square. 9. EFGH is a rectangle.

A B D C ? 5 in. E F H G ? ? 7 cm 2 cm EF 5 cm EH 5 cm

10. PQRS is a square. 11. ABCD is a rectangle.

Its length is twice its width.

P Q S R ? 10 ft A B D C ? 14 yd SR 5 ft AB 5 yd Lesson 11.1 SquaresandRectangles Example BC 5

5

in.

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Draw a line segment to break up each ﬁgure into two rectangles. 12.

13. 14.

Draw a line segment to break up each ﬁgure into one square and one rectangle.

15. 16.

17. 18.

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Lesson 11.2 Properties of SquaresandRectangles

Practice 2 Properties of Squares and Rectangles

All the ﬁgures are rectangles. Find the measures of the unknown angles.

Find the measure of /a.

1. Find the measure of /b.

S T

V U

b 27°

2. Find the measure of /c.

A B D C c 45° Example M N P O a 35°

Measure of

/

a = 90° – 35°

= 55°

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All the ﬁgures are rectangles. Find the measures of the unknown angles. 3. Find the measure of /p.

4. Find the measure of /m. P Q S R 36° 18° p A m 39° B C D 22°

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The ﬁgure is a rectangle. Find the measure of the unknown angle.

5. Find the measure of /s.

W 25° s X Z Y 12°

6. The ﬁgure is made up of a rectangle and a square. Find BC and GE.

A C D B G E F ? 15 cm 12 cm 8 cm ?

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7. The ﬁgure is made up of two rectangles. Find BD and FG.

A C D B G E ? 20 ft 17 ft 14 ft F ? 5 ft

8. The ﬁgure is made up of two rectangles. Find QR and RT.

5 yd P Q R T U V S ? 3 yd 6 yd 4 yd ?

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9. The ﬁgure is made up of two rectangles. Find FG.

5 mi A ? 3 mi 8 mi B D C G H F E

10. The ﬁgure is made up of a square and a rectangle. Find BC.

10 ft A B C D H F _E G 4 ft 2 ft ?

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When we divide a rectangle into two, we get two right triangles.

In the same way, we can divide a square into two right triangles.

11. Which two of these right triangles make a rectangle and which two make a square?

A _B C

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Figure ABCD is a rectangle.

Complete each statement. Use the words in the box.

opposite parallel of equal length right sides four

A

B

C D

1. A rectangle has .

2. Its sides are .

3. Its sides are .

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Challenging Practice

Put On Your Thinking Cap!

1. The ﬁgure is made up of two squares, one with 10-inch sides and the other with 6-inch sides. Find QR.

? P Q R S T U QR 5 in.

2. The ﬁgure is made up of three identical squares with 3-inch sides. Find the total length of BC and FG.

B C

D A

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Problem Solving

Put On Your Thinking Cap!

1. Look at the ﬁgure. What is the least number of squares that must be added to make a rectangle?

2. Draw line segments to divide the ﬁgure into three rectangles in three ways.

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3. Cut out the shaded rectangles and squares. Arrange them to ﬁt inside rectangle A without overlapping. Then attach them with tape.