Quadrilaterals Worksheet With Answers Page 33
ADVERTISEMENT
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
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
503. Given:
PARL with vertices P(-3,-1), A(4,-1), R(4,3), L(x+2,y-3)
Find the value of x and y so that
PARL is a rectangle.
Solutions:
1. a) OT = PR
(The diagonals of a rectangle are congruent.)
7x – 13 = 4x + 11
(Substitution)
3x = 24
(Addition/subtraction property of equality)
x = 8
(Multiplication/division property of equality)
OT = 7 • 8 – 13 = 56 – 13 = 43 in
b) m ∠ TPR + m ∠ RPO = 90 (A rectangle has 1 right ∠ ; complementary
angles have a sum of 90 ° .)
6x + 15 + 5x + 9 = 90 (Substitution)
11x + 24 = 90
11x = 66
x = 6
m ∠ TPR = 6 • 6 + 15 = 36 + 15 = 51
m ∠ RPO = 5 • 6 + 9 = 30 + 9 = 39
∠ TPR + ∠ RPO = ∠ TPO (Angle addition property)
51 + 39 = 90
(Substitution)
m ∠ TPO = 90
2. Since we are given
ANGL, we need to show that this figure has 1 right
angle for it to be a rectangle. Right angles are formed by perpendiculars. By
showing that two sides are perpendicular, we can establish a right angle. We
will use the slopes of two adjacent sides to do this. The following property of
perpendicular lines will be needed.
Property of Perpendicular Lines in the
Coordinate Plane
Two lines are perpendicular if and only if
their slopes have a product of -1 and neither
line is vertical.
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education