6.6 Trapezoids and Midsegment Theorem

Warm up 3 3 2 2 -1 -1 -12 -12 2 2 12 12

Objective: Use properties of trapezoids.

Trapezoid The parallel sides are called the bases. A trapezoid is a quadrilateral with one pair of parallel sides. The parallel sides are called the bases. The non-parallel sides are called the legs.

Properties of Isosceles Trapezoids If a trapezoid is isosceles, then each pair of base angles is congruent.

Properties of Isosceles Trapezoids If a trapezoid has a pair of congruent base angles, then it is isosceles.

1) PQRS is an isosceles trapezoid. Find the missing angle measures. 180-50=130 50 130 130

2) ABCD is an isosceles trapezoid. Find the missing angle measures. 105 105 180-75=105 75

2) ABCD is an isosceles trapezoid. Find the missing angle measures. 100 180-80=105 80 80

Midsegment of a trapezoid: The midsegment of a trapezoid is the segment that connects the midpoints of its legs. Midsegment

PROPERTY OF A MIDSEGMENT of a TRAPEZOID The length of the midsegment is half of the sum of the length of the bases **taking the average** Top + Bottom = midsegment 2

Find the length of the midsegment DG of trapezoid CEFH. c) Top + Bottom = midsegment 2

d) Find the length of the midsegment MN of the trapezoid. Top + Bottom = midsegment 2

e) Find the length of the midsegment MN of the trapezoid. Top + Bottom = midsegment 2

f) Find the length of the midsegment MN of the trapezoid. Top + Bottom = midsegment 2

Example 3: Solve for x. g) 2 2

Example 3: Solve for x. h) 2 2

Example 3: Solve for x. i) 2 2

Example 3: Solve for x. j) 2 2

Example 3: Solve for x. k) 2 2