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GEO 12213.notebook January 22, 2013 Geometry 1/22/13 no because the opposite angles are not congruent. no because the consecutive angles add to 181 6.6, Special Quadrilaterals NAME THE FIGURE THAT IS BEING DESCRIBED: 1. A quadrilateral with exactly one pair of opposite angles congruent and perpendicular diagonals. 2. A quadrilateral that is both a rhombus and a rectangle. 3. A quadrilateral with exactly one pair of parallel sides. 4. Any parallelogram with perpendicular diagonals. Example 1, Identifying Quadrilaterals #1 ABCD has at least two congruent consecutive sides. What quadrilaterals meet this condition? Kite, #2 ABCD has perpendicular diagonals. What quadrilaterals meet this condition? Kite, How do we read this? RELATIONSHIPS FOR QUADRILATERALS quadrilateral kite parallelogram rhombus trapezoid rectangle isosceles trapezoid square Example 2, Identify the special quadrilateral. Use the most specific name. #1 #2 1 GEO 12213.notebook January 22, 2013 Properties of Quadrilaterals Parallelogram • Consecutive angles are supplementary. • Both pairs of opp. angles are congruent. • Diagonals bisect. • Opp. sides are parallel. • Both pairs of opp. sides are congruent. Kite Trapezoid • Exactly one pair of parallel sides(bases) • Two pairs of consecutive angles that are supplementary. 3 2 1 • Two pairs of consecutive sides are congruent. • One pair of opposite angles are congruent. • The diagonals are perpendicular. 4 Rectangle Isosceles Trapezoid • four right angles. • diagonals are congruent. • The base angles are congruent. • The legs are congruent. • The diagonals are congruent. Rhombus • four congruent sides. • diagonals are perpendicular Square • • • • four congruent sides. diagonals are perpendicular four right angles. diagonals are congruent. 2 GEO 12213.notebook January 22, 2013 3