6.5 EQ: How do you Identify a trapezoid and apply its properties?

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Presentation transcript:

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?

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

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.

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.

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

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

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

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

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°

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

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

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