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Properties of Trapezoids - Identifying and Applying

Learn how to identify a trapezoid and apply its properties, including recognizing the parallel sides as bases, the nonparallel sides as legs, and understanding base angles. Explore the concept of isosceles trapezoids and the formula for the midsegment.

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Properties of Trapezoids - Identifying and Applying

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  1. 6.5 • 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.

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

  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.

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

  6. 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.

  7. 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.

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

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

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

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

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

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

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

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

  16. Checkpoint Find Angle Measures of Trapezoids ABCD is an isosceles trapezoid. Find the missing angle measures. 1. 2. 3.

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

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

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

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

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

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

  23. Checkpoint Midsegment of a Trapezoid Find the length of the midsegmentMN of the trapezoid. 4. 5. 6.

  24. Checkpoint Midsegment of a Trapezoid Find the length of the midsegmentMN of the trapezoid. 4. 5. 8 11 21 ANSWER ANSWER ANSWER 6.

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

  26. 3. rectangle ANSWER 4. rectangle ANSWER 5. 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? square ANSWER

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