Quadrilaterals Worksheet With Answers Page 26
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503. a) Show consecutive angles supplementary.
(2x + 14) + (15x – 4) = 180
17x + 10 = 180
17x = 170
x = 10
(2x + 14) = 2 • 10 + 14 = 20 + 14 = 34
(15x – 4) = 15 • 10 – 4 = 150 – 4 = 146
(4x – 6) = 4 • 10 – 6 = 40 – 6 = 34
34 + 146 = 180
When x = 10, consecutive angles are supplementary.
b) Show opposite sides congruent.
2
2
x
+ 3x – 7 = x
-2x + 18
3x – 7 = -2x + 18
5x = 25
x = 5
+ 3 • 5 – 7 = 25 + 15 -7 = 33
2
2
x
+ 3x – 7 = 5
-2 • 5 + 18 = 25 – 10 + 18 = 33
2
2
x
-2x + 18 = 5
5x + 12 = 5 • 5 + 12 = 25 + 12 = 37
4.
Statements
Reasons
1. Quadrilateral ABCD
1. Given
∠ A and ∠ B are supplementary
∠ A and ∠ D are supplementary
2. If two lines are cut by a
2. AD
BC
transversal so that the interior
angles on the same side are
supplementary, then the lines
are parallel.
3. AB
DC
3. If two lines are cut by a transversal
so that the interior angles on the
same side are supplementary, then
the lines are parallel.
4. If the opposite sides of a
4. Quadrilateral ABCD is a
quadrilateral are parallel, then
the quadrilateral is a
parallelogram.
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