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created by chris markstrum © 2005 6.6 Specialized Quadrilaterals California State Standards for Geometry 7: Prove & use theorems involving parallel lines and properties of quadrilaterals. 8: Solve problems involving perimeter and area. 10: Compute area of polygons 12: Find and use measures of sides and angles of triangles and polygons quadrilateral relationships Quadrilaterals trapezoids parallelograms kites squares created by chris markstrum 2005 created by chris markstrum 2005 quadrilateral relationships quadrilateral kite parallelogram rhombus rectangle square trapezoid isosceles trapezoid Example created by chris markstrum 2005 A quadrilateral has at least one pair of opposite sides congruent. What kind of quadrilateral is it? quadrilateral kite parallelogram rhombus rectangle square trapezoid isosceles trapezoid Examples created by chris markstrum 2005 A quadrilateral has at least two congruent consecutive sides. What kind of quadrilateral is it? quadrilateral kite parallelogram rhombus rectangle square trapezoid isosceles trapezoid Example created by chris markstrum 2005 The coordinates of a quadrilateral are (-2, 5), (1, 8), (4, 5), and (1, 2) What kind of quadrilateral is it? Explain. y AB BC CD AD 3 2 B m AB 1 C A mBC 1 D x The quadrilateral is a square Example created by chris markstrum 2005 In quadrilateral RSTV, mR 88, mS 113, mV 113 What kind of quadrilateral is it? Explain quadrilateral kite parallelogram rhombus rectangle square trapezoid isosceles trapezoid Example created by chris markstrum 2005 In quadrilateral RSTV, mR 88, mS 113, mV 113 What kind of quadrilateral is it? Explain S R kite 88o S V 113o 113o V R and S are not supplementary. 46o T created by chris markstrum 2005 quadrilateral properties Property Both pairs of opp. sides // X X X X sorry sorry Exactly one pair of opp. sides are // sorry sorry sorry sorry sorry Both pairs of opp. sides are X X X X sorry sorry Exactly 1 pair of opp. sides are sorry sorry sorry sorry sorry All sides are congruent sorry sorry X X X sorry sorry created by chris markstrum 2005 quadrilateral properties Property X X X sorry X sorry sorry X X X X sorry sorry X X X X sorry sorry Diagonals are perpendicular sorry sorry Diagonals are congruent sorry Diagonals bisect each other Both pairs of opp. angles are Exactly one pair of opp angles are sorry sorry sorry sorry All angles are congruent sorry X sorry X X X sorry sorry sorry sorry Summary What characteristics must be considered when classifying a quadrilateral? Why must a parallelogram with one right angle be a rectangle? created by chris markstrum 2005

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