In an trapezoid, there can be, at most, two congruent sides. Is this true or false?
Hint
What other theorems about congruent sides of quadrilaterals have we shown?
Answer
True
Example 2
Prove that the diagonals of an isosceles trapezoid are congruent.
Hint
Prove the two triangles with diagonals as sides are congruent.
Answer
Statements
Reasons
1. PQRS is an isosceles trapezoid
Given
2. PS ≅ RQ
Definition of an isosceles trapezoid (1)
3. ∠SPQ ≅ ∠RQP
Base angles of an isosceles trapezoid are congruent (1)
4. PQ ≅ PQ
Reflexive Property
5. ΔRPQ ≅ ΔSPQ
SAS Postulate (2, 3, 4)
6. PR ≅ SQ
CPCTC (5)
Example 3
Calculate the perimeter of trapezoid RENA.
Hint
The Pythagorean Theorem might help you out a bit here. To find the length of NE, anyway.
Answer
34 units
Example 4
Calculate the measures of the unmarked angles of the isosceles trapezoid FGHI.
Hint
What are the properties of the isosceles trapezoid?
Answer
m∠G = 30°, m∠H = m∠I = 150°
Example 5
Calculate the perimeter of the trapezoid JKLM to the nearest whole number.
Hint
Use the Pythagorean Theorem. Yes, we know these aren't triangles.
Answer
53 units
Example 6
In the figure, trapezoid BCDF has median RS, and PQ is the median of trapezoid RSDF. What is the length of PQ in terms of x?
Hint
Simon says, "Apply the median formula for trapezoid BCDF." Simon says, "Apply the median formula for trapezoid RSDF." Then, do the Hokey Pokey. But wait—Simon didn't say!
