1. 6.5 EQ: How do you Identify a trapezoid and apply its properties?
Use properties of trapezoids.
EQ: How do you Identify a trapezoid and apply its properties?

2. trapezoid A quadrilateral with exactly one pair of parallel sides.
The parallel sides are called the bases.
The nonparallel sides are called the legs.

3. trapezoid A quadrilateral with exactly one pair of parallel sides.
The parallel sides are called the bases.
The nonparallel sides are called the legs.
A trapezoid has two pairs of base angles.

4. trapezoid A quadrilateral with exactly one pair of parallel sides.
The parallel sides are called the bases.
The nonparallel sides are called the legs.
A trapezoid has two pairs of base angles.

6. isosceles trapezoid.
If the legs of a trapezoid are congruent.

7. Theorem 6.12
If a trapezoid is isosceles, then each pair of base angles is congruent.

8. Theorem 6.13
If a trapezoid has a pair of congruent base angles, then it is isosceles.

9. PQRS is an isosceles trapezoid. Find the missing angle measures.
Example 1
Find Angle Measures of Trapezoids
PQRS is an isosceles trapezoid. Find the missing angle measures.
SOLUTION
PQRS is an isosceles trapezoid
So, mR = mS = 50°. 1.
Because S and P are same-side interior angles & are supplementary. So, mP = 180° – 50° = 130°. 2.
Because Q and P are a pair of base angles of an isosceles trapezoid, mQ = mP = 130°. 3. 9

10. ABCD is an isosceles trapezoid. Find the missing angle measures.
Checkpoint
Find Angle Measures of Trapezoids
ABCD is an isosceles trapezoid. Find the missing angle measures. 1.
ANSWER
mA = 80°; mB = 80°; mC = 100° 2.
ANSWER
mA = 110°; mB = 110°; mD = 70° 3.
ANSWER
mB = 75°; mC = 105°; mD = 105°

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

13. Find the length of the midsegment DG of trapezoid CEFH.
Example 2
Midsegment of a Trapezoid
Find the length of the midsegment DG of trapezoid CEFH.
SOLUTION
Use the formula for the midsegment of a trapezoid.
DG = 1 2
(EF + CH)
Formula for midsegment of a trapezoid = 1 2
(8 + 20)
Substitute 8 for EF and 20 for CH. = 1 2
(28)
Add.
= 14
Multiply.
ANSWER
The length of the midsegment DG is 14. 13

14. Find the length of the midsegment MN of the trapezoid.
Checkpoint
Midsegment of a Trapezoid
Find the length of the midsegment MN of the trapezoid. 4.
ANSWER 11 5.
ANSWER 8 6.
ANSWER 21