Quadrilaterals Worksheet With Answers Page 46
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502. Given: Isosceles trapezoid CAMT
T
M
m∠T = 8x – 10
m∠M = 5x + 20
Find:
x = ________
m∠T = ________
C
A
m∠C = ________
3. Given: Trapezoid WORK with vertices W(-2,-1), O(6,-1), R(4,3)
a) Graph trapezoid WORK in the coordinate plane.
b) Find the coordinates of vertex K so that trapezoid WORK is isosceles.
Solutions:
1.
Statements
Reasons
1. Isosceles trapezoid TRAP
1. Given
TP ≅
2. Definition of an isosceles
2.
AR
trapezoid
3. ∠PTR ≅ ∠ART
3. The base angles of an isosceles
trapezoid are congruent.
TR ≅
4.
TR
4. Reflexive property
5. ∆ PTR ≅ ∆ ART
5. SAS congruence postulate
6. ∴ ∠TPR ≅ ∠RAT
6. CPCTC
m∠T = ∠M
(Base angles of an isosceles trapezoid ≅)
2.
8x – 10 = 5x + 20
(Substitution)
3x = 30
(Addition/subtraction properties of equality)
x = 10
(Division/multiplication properties of equality)
m∠T = 8•10 – 10 = 80-10 = 70
m∠C = 180 – 70 = 110
3. b) Vertex K has the coordinates (0,3).
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