Trapezoids and Kites Skill 32 Objective HSGCO 11

Trapezoids and Kites Skill 32

Objective HSG-CO. 11: Students are responsible for verifying and using properties of trapezoids and kites.

Definitions A trapezoid is a quadrilateral with exactly one pair of parallel sides. The parallel sides of a trapezoid are called the bases of the trapezoid. The nonparallel sides are called the legs of the trapezoid. The two angles that share a base a trapezoid are called the base angles. Bases Legs

Definitions An isosceles trapezoid is a trapezoid with legs that are congruent. The midsegment of a trapezoid is the segment that joins the midpoints of the legs of a trapezoid. A kite is a quadrilateral with two pairs of consecutive sides congruent and no opposite sides congruent.

Thm. 56: Isosceles Trapezoid – Base Angles Congruent If a quadrilateral is an isosceles trapezoid, then each pair of base angles is congruent. A D B C

Thm. 57: Isosceles Trapezoid – Diagonals Congruent If a quadrilateral is an isosceles trapezoid, then its diagonals are congruent. A D B C

Thm. 58: Trapezoid Midsegment Theorem If a quadrilateral is a trapezoid, then the midsegment is parallel to its bases and the length of the midsegment is half the sum of the lengths of the bases. A E D B F C

Thm. 59: Kite – Diagonals Perpendicular If a quadrilateral is a kite, then its diagonals are perpendicular. B A C D

Example 1; Finding Angle Measures of Trapezoids D C 65ᵒ E F

Example 1; Finding Angle Measures of Trapezoids Q 106ᵒ R S P

Example 2; Using Midsegment of a Trapezoid L M Q P R 8 N

Example 2; Using Midsegment of a Trapezoid Q M P 10 R N S

Example 3; Finding Angle Measures of a Kite-Diagonals ⏊ (Thm. 59) ∆ ∠ Sum (Thm. 16) D SSS Postulate C. P. C. T. E G F

Example 3; Finding Angle Measures of a Kite-Diagonals ⏊ (Thm. 59) ∆ ∠ Sum (Thm. 16) SSS Postulate C. P. C. T. L M K N

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