Quadrilaterals Worksheet With Answers Page 45
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50We will consider two theorems relating to an isosceles trapezoid as follows.
Isosceles Trapezoid Theorem
If a trapezoid is isosceles, then
the base angles are congruent.
Isosceles Trapezoid Theorem
If a trapezoid is isosceles, then
the diagonals are congruent.
These theorems will be applied in the following examples.
Examples
1. Given: Isosceles trapezoid TRAP
Prove: ∠TPR ≅ ∠RAT
Complete the proof with the appropriate statements and reasons.
P
A
T
R
Proof:
Statements
Reasons
1. Isosceles trapezoid TRAP
1. __________________________
TP ≅
2. __________________________
2.
AR
3. ∠PTR ≅ ∠ART
3. __________________________
4. Reflexive property
4. __________________________
5. __________________________
5. __________________________
6. __________________________
6. ∴ ∠TPR ≅ ∠RAT
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