Quadrilaterals Exercises

Example 1

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?

Example 2

Prove that the diagonals of an isosceles trapezoid are congruent.

Hint

Prove the two triangles with diagonals as sides are congruent.

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.

Example 4

Calculate the measures of the unmarked angles of the isosceles trapezoid FGHI.

Hint

What are the properties of the isosceles trapezoid?

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.

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!

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)

Quadrilaterals Exercises

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

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