1.
7.1 × 38
2.
0.48 × 2.7
3.
20 × 5.2
4.
0.51 × 43
5.
1.0 × 69
6.
4.6 × 82
7.
2.5 × 34
8.
64 × 66
9.
0.94 × 5.0
10.
0.012 × 5.7
11.
62 × 80
12.
2.0 × 39
13.
0.13 × 26
14.
0.51 × 85
15.
39 × 33
16.
4.4 × 2.6
17.
0.014 × 46
18.
0.018 × 41
19.
0.089 × 16
20.
2.4 × 5.3
21.
0.38 × 1.8
22.
54 × 88
23.
3.0 × 89
24.
73 × 42
25.
0.20 × 7.3
26.
8.1 × 3.5
27.
0.33 × 6.0
28.
0.052 × 9.7
29.
0.45 × 5.4
30.
0.055 × 30
31.
0.068 × 8.8
32.
11 × 2.3
33.
9.2 × 84
34.
0.057 × 23
35.
6.2 × 39
-1-
1.
7.1 × 38 269.8
2.
0.48 × 2.7 1.296
3.
20 × 5.2 104.0
4.
0.51 × 43 21.93
5.
1.0 × 69 69.0
6.
4.6 × 82 377.2
7.
2.5 × 34 85.0
8.
64 × 66 4,224
9.
0.94 × 5.0 4.700
10.
0.012 × 5.7 0.0684
11.
62 × 80 4,960
12.
2.0 × 39 78.0
13.
0.13 × 26 3.38
14.
0.51 × 85 43.35
15.
39 × 33 1,287
16.
4.4 × 2.6 11.44
17.
0.014 × 46 0.644
18.
0.018 × 41 0.738
19.
0.089 × 16 1.424
20.
2.4 × 5.3 12.72
21.
0.38 × 1.8 0.684
22.
54 × 88 4,752
23.
3.0 × 89 267.0
24.
73 × 42 3,066
25.
0.20 × 7.3 1.460
26.
8.1 × 3.5 28.35
27.
0.33 × 6.0 1.980
28.
0.052 × 9.7 0.5044
29.
0.45 × 5.4 2.430
30.
0.055 × 30 1.650
31.
0.068 × 8.8 0.5984
32.
11 × 2.3 25.3
33.
9.2 × 84 772.8
34.
0.057 × 23 1.311
35.
6.2 × 39 241.8
-1-
A.
1.
3.9 × 8.3
2.
47 × 17
3.
99 × 45
4.
0.80 × 2.2
5.
2.1 × 64
6.
41 × 61
7.
0.52 × 7.4
8.
0.64 × 8.6
9.
0.13 × 88
10.
8.3 × 9.3
11.
2.1 × 2.0
12.
5.3 × 82
13.
70 × 6.0
14.
9.3 × 2.0
15.
92 × 4.3
16.
0.081 × 84
17.
16 × 29
18.
2.2 × 9.3
19.
0.057 × 74
20.
2.3 × 44
21.
0.69 × 2.6
22.
0.071 × 70
23.
1.1 × 67
24.
5.0 × 70
25.
0.70 × 58
26.
8.1 × 7.2
27.
0.80 × 31
28.
5.1 × 77
29.
7.5 × 98
30.
44 × 95
31.
4.4 × 57
32.
34 × 33
33.
1.7 × 3.1
34.
0.022 × 8.0
35.
0.037 × 6.5
-1-
A.
1.
3.9 × 8.3 32.37
2.
47 × 17 799
3.
99 × 45 4,455
4.
0.80 × 2.2 1.760
5.
2.1 × 64 134.4
6.
41 × 61 2,501
7.
0.52 × 7.4 3.848
8.
0.64 × 8.6 5.504
9.
0.13 × 88 11.44
10.
8.3 × 9.3 77.19
11.
2.1 × 2.0 4.20
12.
5.3 × 82 434.6
13.
70 × 6.0 420.0
14.
9.3 × 2.0 18.60
15.
92 × 4.3 395.6
16.
0.081 × 84 6.804
17.
16 × 29 464
18.
2.2 × 9.3 20.46
19.
0.057 × 74 4.218
20.
2.3 × 44 101.2
21.
0.69 × 2.6 1.794
22.
0.071 × 70 4.970
23.
1.1 × 67 73.7
24.
5.0 × 70 350.0
25.
0.70 × 58 40.60
26.
8.1 × 7.2 58.32
27.
0.80 × 31 24.80
28.
5.1 × 77 392.7
29.
7.5 × 98 735.0
30.
44 × 95 4,180
31.
4.4 × 57 250.8
32.
34 × 33 1,122
33.
1.7 × 3.1 5.27
34.
0.022 × 8.0 0.1760
35.
0.037 × 6.5 0.2405
-1-
1.
2.7 × 98
2.
76 × 37
3.
4.6 × 2.5
4.
67 × 8.8
5.
7.5 × 3.6
6.
9.3 × 6.7
7.
0.99 × 2.0
8.
0.13 × 63
9.
0.043 × 72
10.
4.6 × 6.2
11.
9.0 × 98
12.
3.4 × 9.0
13.
0.30 × 70
14.
65 × 9.7
15.
0.67 × 11
16.
9.3 × 64
17.
0.039 × 68
18.
0.19 × 6.5
19.
9.3 × 2.4
20.
3.0 × 43
21.
5.6 × 1.0
22.
0.81 × 7.6
23.
19 × 5.1
24.
76 × 73
25.
0.91 × 4.4
26.
83 × 45
27.
5.5 × 4.9
28.
89 × 17
29.
74 × 8.1
30.
2.2 × 40
31.
8.6 × 99
32.
5.9 × 1.9
33.
0.38 × 85
34.
7.6 × 8.4
35.
2.5 × 6.2
-1-
1.
2.7 × 98 264.6
2.
76 × 37 2,812
3.
4.6 × 2.5 11.50
4.
67 × 8.8 589.6
5.
7.5 × 3.6 27.00
6.
9.3 × 6.7 62.31
7.
0.99 × 2.0 1.980
8.
0.13 × 63 8.19
9.
0.043 × 72 3.096
10.
4.6 × 6.2 28.52
11.
9.0 × 98 882.0
12.
3.4 × 9.0 30.60
13.
0.30 × 70 21.00
14.
65 × 9.7 630.5
15.
0.67 × 11 7.37
16.
9.3 × 64 595.2
17.
0.039 × 68 2.652
18.
0.19 × 6.5 1.235
19.
9.3 × 2.4 22.32
20.
3.0 × 43 129.0
21.
5.6 × 1.0 5.60
22.
0.81 × 7.6 6.156
23.
19 × 5.1 96.9
24.
76 × 73 5,548
25.
0.91 × 4.4 4.004
26.
83 × 45 3,735
27.
5.5 × 4.9 26.95
28.
89 × 17 1,513
29.
74 × 8.1 599.4
30.
2.2 × 40 88.0
31.
8.6 × 99 851.4
32.
5.9 × 1.9 11.21
33.
0.38 × 85 32.30
34.
7.6 × 8.4 63.84
35.
2.5 × 6.2 15.50
-1-
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
-1-
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
-2-
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
-1-
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
-2-
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Lesson 45
223
L E S S O N
45
Classifying Quadrilaterals
NEW CONCEPT Recall from Lesson 32 that a quadrilateral is a polygon with four sides. Although all quadrilaterals have four sides, quadrilaterals have many different shapes. Here is an assortment of quadrilaterals:
We can classify (sort) quadrilaterals into different types, such as squares, rectangles, parallelograms, and trapezoids. In this lesson we will learn ways to sort quadrilaterals, and we will practice drawing named quadrilaterals. One way quadrilaterals are sorted is by parallel sides. Recall that parallel segments run in the same direction and remain the same distance apart. Here we show three pairs of parallel segments:
224
Saxon Math 6/5
If we put the left-hand pair of segments with the center pair, we get this quadrilateral:
If we put the right-hand pair with the center pair, we get this quadrilateral:
Both of these quadrilaterals have two pairs of parallel sides. Below we show some more quadrilaterals with two pairs of parallel sides. Use a finger or the eraser of your pencil to trace the pairs of parallel sides on each quadrilateral. Notice that the two segments that form a parallel pair are the same length. These quadrilaterals are called parallelograms.
Parallelograms
Parallelograms are quadrilaterals with two pairs of parallel sides and are one classification of quadrilaterals. Quadrilaterals
Parallelograms
Trapezoids
Trapeziums
Trapezoids are another type of quadrilateral. Trapezoids have only one pair of parallel sides (the other pair of sides are not parallel). Here are some examples of trapezoids. First trace the parallel sides, and then trace the sides that are not parallel. Notice that the parallel segments in each figure are not the same length.
Trapezoids
Lesson 45
225
Some quadrilaterals have no parallel sides. In the United States we call these shapes trapeziums.
Trapeziums
Example 1 Draw an example of a parallelogram, a trapezoid, and a trapezium. Solution To draw a parallelogram, we may begin by drawing two parallel segments of the same length.
Then we draw two more segments between the endpoints. We check these two segments to be sure they are parallel.
Parallelogram
This parallelogram happens to look like a rectangle. As we will see in a moment, rectangles are a special type of parallelogram. To draw a trapezoid, we may begin by drawing two parallel segments of different lengths.
Then we draw two more segments between the endpoints.
Trapezoid
To draw a trapezium, we may begin by drawing two segments that are not parallel and do not intersect.
226
Saxon Math 6/5
Then we draw two segments between the endpoints. We check that these two segments are not parallel.
Trapezium
There are different categories of parallelograms, trapezoids, and trapeziums. In this lesson we will look at three types of parallelograms. They are rectangles, rhombuses, and squares. Classifications of Quadrilaterals Quadrilaterals
Parallelograms
Rectangles
Trapezoids
Trapeziums
Rhombuses
Squares
A parallelogram with four congruent angles is a rectangle. Each angle of a rectangle is a right angle.
Rectangles
A parallelogram with four congruent sides (four sides of equal length) is a rhombus. Some people refer to a rhombus as a â&#x20AC;&#x153;diamond.â&#x20AC;? A rhombus is an equilateral quadrilateral (just like a triangle with all sides of equal length is an equilateral triangle).
Rhombuses
Lesson 45
227
Notice that a square is both a rectangle and a rhombus. A square has four right angles and four congruent sides. Example 2 A square is not which of the following? A. parallelogram
B. rhombus
C. rectangle
D. trapezoid
Solution A square is a quadrilateral with parallel sides of equal length that intersect at right angles. So a square is a parallelogram, a rhombus, and a rectangle. A square is not a D. trapezoid.
LESSON PRACTICE Practice set The words parallelogram, trapezoid, trapezium, rectangle, rhombus, and square were used in this lesson to describe quadrilaterals. Use every word that applies to describe each quadrilateral below. a. b. c.
d.
e.
f.
g. Describe the difference between a parallelogram and a trapezoid. h. Draw a rhombus that does not have right angles.
MIXED PRACTICE Problem set
1. Draw a rectangle with all sides the same length. (45)
For problems 2â&#x20AC;&#x201C;4, write an equation and find the answer. 2. Julie paid $10 and got back $2.47. How much money did (16) she spend? 3. Each of the fifty states has two U.S. senators. Altogether, how many U.S. senators are there?
(21)
4. The Phantom of the Opera was a hit. The theater was filled all 4 nights. If 2500 attended in all, then how many attended each night?
(21)