z Trapezoids and Kites Section 6 6 Goals

Goals: z § Friday: Trapezoids § § Discussed: Kites § Definition § Vocabulary terms

z Trapezoids: § Definition: § A quadrilateral with exactly one pair of parallel sides

z Isosceles Trapezoids: § Definition: § A quadrilateral with exactly one pair of parallel

z Kites: § Definition: § A quadrilateral with exactly two pair of consecutive congruent

z New Properties: Trapezoids Theorems 6. 21 -6. 24:

z Theorem 6. 21: § If a trapezoid is isosceles, then each pair of

z Theorem 6. 22: CONVERSE OF THEOREM 6. 21 § If a trapezoid has

z Theorem 6. 23: § A trapezoid is isosceles if and only if its

z Midsegment: § Definition: § A segment that connects the midpoints of the legs

z Theorem 6. 24: § The midsegment of a trapezoid is parallel to each

z New Properties: Kites Theorems 6. 25 -6. 25:

z Theorem 6. 25: § If a quadrilateral is a kite, then its diagonals

z Theorem 6. 26: § If a quadrilateral is a kite, then exactly one

Homework: z Continue to work on adding theorems to your mind map. Bubbl. us

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z Trapezoids and Kites Section 6. 6

Goals: z § Friday: Trapezoids § § Discussed: Kites § Definition § Vocabulary terms Review: trapezoids § Theorems 6. 21 -6. 24 § New: kites § Theorems 6. 25 -6. 26

z Examples:

z Trapezoids: § Definition: § A quadrilateral with exactly one pair of parallel sides § Vocabulary terms: § Bases: parallel sides of the trapezoid § Legs: non parallel sides § Base Angles: angle formed by one base and one leg

z Isosceles Trapezoids: § Definition: § A quadrilateral with exactly one pair of parallel sides and the other pair are congruent. § Vocabulary terms: § Bases: parallel sides of the trapezoid § Legs: congruent non-parallel sides § Base Angles: angle formed by one base and one leg

z Example: sketch

z Kites: § Definition: § A quadrilateral with exactly two pair of consecutive congruent sides. § Unlike a parallelogram, the opposite sides are non congruent.

z Example: sketch

z Example: Fill in the blank

z New Properties: Trapezoids Theorems 6. 21 -6. 24:

z Theorem 6. 21: § If a trapezoid is isosceles, then each pair of base angles are congruent. § Proof: § Postulate 3. 6: P. 215 § Page 218

z Theorem 6. 22: CONVERSE OF THEOREM 6. 21 § If a trapezoid has one pair of congruent base angles, then it is an isosceles trapezoid. § Proof:

z Theorem 6. 23: § A trapezoid is isosceles if and only if its diagonals are congruent. § Proof:

z Midsegment: § Definition: § A segment that connects the midpoints of the legs of a trapezoid.

z Example: sketch

z Theorem 6. 24: § The midsegment of a trapezoid is parallel to each base and its measure is one half the sum of the lengths of the bases. § Example:

z Example: sketch

z New Properties: Kites Theorems 6. 25 -6. 25:

z Theorem 6. 25: § If a quadrilateral is a kite, then its diagonals are perpendicular. § Proof:

z Theorem 6. 26: § If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent. § Proof:

Homework: z Continue to work on adding theorems to your mind map. Bubbl. us P. 444 #1, 2, 6 -11, 16 -21, 24 -27