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.

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

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.

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.

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

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 6.12 If a trapezoid is isosceles, then each pair of base angles is 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 and R and S are a pair of base angles. So, mR = mS = 50°. 1. Because S and P are same-side interior angles formed by parallel lines, they 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. 16

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. 2. 3.

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.

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

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

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. 24

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. 5. 6.

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

Use the information in the diagram to name the special quadrilateral. 1. ANSWER rhombus 2. ANSWER rhombus

3. ANSWER rectangle 4. ANSWER rectangle Kim arranges four metersticks to make a parallelogram. Then she adjusts the metersticks so that each pair meets at a right angle. What shape has Kim formed? 5. ANSWER square