Quadrilaterals Worksheet With Answers Page 7
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50b) m ∠ F = (8x - 15)
9
m ∠ D = (
x + 45)
2
m ∠ E = (5x + 21)
x = ________
m ∠ D = ________
m ∠ R = ________
3. Given: Quadrilateral PQRS with three vertices P(-2,3), Q(4,3), and S(0,8)
a) Graph these vertices in the coordinate plane.
b) Determine the coordinates of vertex R so that the quadrilateral is a
parallelogram.
4. Given: Quadrilateral RSTV with vertices R(5,1), S(8,3), T(4,7), and V(1,5)
a) Graph quadrilateral RSTV in the coordinate plane.
b) Show quadrilateral RSTV is a parallelogram.
5. Given:
EFGH
H
J
G
HI ⊥
EF
JF ⊥
HG
≅
Prove: HI
JF
E
I
F
Write a paragraph, two-column, or flow-chart proof.
Solutions:
1. a) DC
AB
Definition of a parallelogram.
b) ∠ ADC ≅ ∠ ABC
are ≅ .
The opposite angles of a
c) ∠ DCA ≅ ∠ BAC
If 2 parallel lines are cut by a transversal,
then the alternate interior angles are
congruent
≅
are ≅ .
d)
AD
BC
The opposite sides of a
e) ∆ ADC ≅ ∆ CBA
SSS, SAS, or ASA congruence postulates;
or AAS congruence theorem
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