1. 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

2. created by chris markstrum 2005 quadrilateral relationships Quadrilaterals parallelograms rectangles rhombi squaressquares squaressquares trapezoids kites

3. created by chris markstrum 2005 quadrilateral relationships quadrilateral kiteparallelogramtrapezoid rhombusrectangle square isosceles trapezoid

4. created by chris markstrum 2005 Example A quadrilateral has at least one pair of opposite sides congruent. What kind of quadrilateral is it? parallelogram rhombusrectangle square trapezoid isosceles trapezoid kite quadrilateral

5. created by chris markstrum 2005 Examples A quadrilateral has at least two congruent consecutive sides. What kind of quadrilateral is it? parallelogram rhombus rectangle square trapezoid isosceles trapezoid kite quadrilateral sometimes

6. created by chris markstrum 2005 B C D A Example The coordinates of a quadrilateral are (-2, 5), (1, 8), (4, 5), and (1, 2) What kind of quadrilateral is it? Explain. x y The quadrilateral is a square

7. created by chris markstrum 2005 Example In quadrilateral RSTV, What kind of quadrilateral is it? Explain parallelogram rhombusrectangle square trapezoid isosceles trapezoid kite quadrilateral

8. created by chris markstrum 2005 In quadrilateral RSTV, What kind of quadrilateral is it? Explain kite R S 88 o 113 o V T 46 o and are not supplementary. Example

9. created by chris markstrum 2005 Property sorry only isosceles XXXX X XX XX XX sorry Both pairs of opp. sides // Exactly one pair of opp. sides are // Both pairs of opp. sides are Exactly 1 pair of opp. sides are All sides are congruent quadrilateral properties

10. created by chris markstrum 2005 Property sorry X X X XXX X X X X X XXXX X Diagonals are perpendicular Diagonals are congruent Diagonals bisect each other Both pairs of opp. angles are Exactly one pair of opp angles are All angles are congruent quadrilateral properties

11. created by chris markstrum 2005 Summary What characteristics must be considered when classifying a quadrilateral? Why must a parallelogram with one right angle be a rectangle?