1. 5.5 Properties of Quadrilaterals Objective: After studying this section, you will be able to identify some properties of: a. parallelograms, b. rectangles, c. kites, d. rhombuses, e. squares, and f. isosceles triangles.

2. Properties of Parallelograms 1. Opposite sides are parallel by definition 2. Opposite sides are congruent 3. Opposite angles are congruent 1 32 4 angles 1 and 3 are congruent; angles 2 and 4 are congruent 4. Diagonals bisect each other 5. Any pair of consecutive angles are supplementary

3. Properties of Rectangles 1. All the properties of a parallelogram apply by definition. 2. All angles are right angles 3. Diagonals are congruent

4. Properties of Kites 1. Two disjoint pair of consecutive sides are congruent by definition 2. Diagonals are perpendicular 3. One diagonal is the perpendicular bisector of the other 4. One of the diagonals bisects a pair of opposite angles 5. One pair of opposite angles are congruent

5. Properties of Rhombuses 1. All properties of a parallelogram apply by definition 2. All properties of a kite apply 3. All sides are congruent (equilateral) 4. Diagonals bisect the angles 5. Diagonals are perpendicular bisectors of each other 6. Diagonals divide the rhombus into four congruent right triangles

6. Properties of Squares 1. All the properties of a rectangle apply by definition 2. All the properties of a rhombus apply by definition 3. Diagonals form four isosceles right triangles

7. Properties of Isosceles Trapezoid 1. Legs are congruent by definition 2. Bases are parallel by definition 3. Lower base angles are congruent 4. Upper base angles are congruent 5. Diagonals are congruent 6. Any lower base angle is supplementary to any upper base angle

8. 1. 2. 3. 4. 5. 6. 7. 8. 9. Given: ABCD is a parallelogram Conclusion: B C E A D F G H 1. 2. 3. 4. 5. 6. 7. 8. 9.

9. Given: VRZA is a parallelogram Find: The perimeter of VRZA R Z V A AV = 2x - 4 VR = 3y + 5 RZ = 1/2x + 8 ZA = y + 12

10. Given: ABCD is a parallelogram Prove: AC and BD bisect each other C D B A 3 E 2 4 1 1. 2. 3. 4. 5. 6. 7. 8. 9. 1. 2. 3. 4. 5. 6. 7. 8. 9.

11. Summary Draw each of the figures and apply the properties in a foldable. Homework: worksheet