1. Unit 6 – Polygons and Quadrilaterals 6.5 Conditions for Special Quads
Objective
Prove that a given quadrilateral is a rectangle, rhombus, or square.

2. Conditions for rectangles:
Unit 6 – Polygons and Quadrilaterals Conditions for Special Quads
Conditions for rectangles:
1. If one angle of a parallelogram is 90°, then it is a rectangle.
2. If the diagonals of a parallelogram are , then it is a rectangle.

3. Conditions for rhombus:
Unit 6 – Polygons and Quadrilaterals Conditions for Special Quads
Conditions for rhombus:
If one pair of consecutive sides of a parallelogram are , then it is a rhombus.
If the diagonals of a parallelogram are ⊥, then it is a rhombus.
If the diagonals of a parallelogram bisect a pair of opposite angles, then it is a rhombus.
What must you show for a quadrilateral to be a square?.

4. Choose the best name for the parallelogram then find the numbered angles.1. 2. 4. 3.

5. How to determine if a parallelogram is a rhombus, rectangle or square
Unit 6 – Polygons and Quadrilaterals Conditions for Special Quads
How to determine if a parallelogram is a rhombus, rectangle or square
Test the diagonals to determine they are equal, perpendicular or both.
If ⊥ then rhombus
If ≌ then rectangle
If both then square
If neither then parallelogram

6. Unit 6 – Polygons and Quadrilaterals 6.5 Conditions for Special Quads
Use the diagonals to determine whether a parallelogram with the given vertices is a rectangle, rhombus, or square. Give all the names that apply.
P(–1, 4), Q(2, 6), R(4, 3), S(1, 1)

7. Unit 6 – Polygons and Quadrilaterals 6.5 Conditions for Special Quads
Use the diagonals to determine whether a parallelogram with the given vertices is a rectangle, rhombus, or square. Give all the names that apply.
W(0, 1), X(4, 2), Y(3, –2), Z(–1, –3)

8. Objectives Vocabulary
Unit 6 – Polygons and Quadrilaterals Kites and Trapezoids
Objectives
Use properties of kites and trapezoids to solve problems.
Vocabulary
kite
trapezoid
base of a trapezoid
leg of a trapezoid
base angle of a trapezoid
isosceles trapezoid
midsegment of a trapezoid

9. Diagonals are perpendicular Theorem Exactly one pair of opp  
Unit 6 – Polygons and Quadrilaterals Kites and Trapezoids
A kite is a quadrilateral with exactly two pairs of congruent consecutive sides.
Theorem
Diagonals are perpendicular
Theorem
Exactly one pair of opp  

10. Find the measures of the numbered angles of each rhombus.
Unit 6 – Polygons and Quadrilaterals Kites and Trapezoids
Find the measures of the numbered angles of each rhombus.
1 = 60°
Diagonals of rhombus bisect angle
Diagonals of rhombus perpendicular to each other
2 = 90° 2 3 4
Angle 3 = 30°
Diagonals of rhombus bisect angle
Base angles .
Angle 3 =
60° 1

11. Unit 6 – Polygons and Quadrilaterals 6.6 Kites and Trapezoids
In kite ABCD, mDAB = 54°, and mCDF = 52°. Find all angle measures possible.

12. Unit 6 – Polygons and Quadrilaterals 6.6 Kites and Trapezoids
A trapezoid is a quadrilateral with exactly one pair of parallel sides. Each of the parallel sides is called a base. The nonparallel sides are called legs. Base angles of a trapezoid are two consecutive angles whose common side is a base.
If the legs of a trapezoid are congruent, the trapezoid is an isosceles trapezoid. The following theorems state the properties of an isosceles trapezoid.

13. The base angles of an isosceles trapezoid are congruent.
Unit 6 – Polygons and Quadrilaterals Kites and Trapezoids
Theorem
The base angles of an isosceles trapezoid are congruent.
The diagonals of an isosceles trapezoid are congruent.
If a trapezoid has one pair of base angles congruent, then it is an isosceles trapezoid.

14. Find the measures of the numbered angles in each isosceles trapezoid.1. 2. 4. 3.

15. JN = 10.6, and NL = 14.8. Find KM. KB = 21.9 and MF = 32.7. Find FB.
Unit 6 – Polygons and Quadrilaterals Kites and Trapezoids
JN = 10.6, and NL = Find KM.
KB = 21.9 and MF = 32.7.
Find FB.

16. The midsegment is half the sum of the bases.
Unit 6 – Polygons and Quadrilaterals Kites and Trapezoids
The midsegment of a trapezoid is the segment whose endpoints are the midpoints of the legs. In Lesson 5-1, you studied the Triangle Midsegment Theorem. The Trapezoid Midsegment Theorem is similar to it.
Theorem
The midsegment is half the sum of the bases.

17. Unit 6 – Polygons and Quadrilaterals 6.6 Kites and Trapezoids
Find EF. 15
Find AD.

18. HOMEWORK:
6.5(434): 9-16,24-26,40
10)rhombus 12)parallelogram 14)parallelogram 16)parallelogram,rhombus 24) )6.5 40)rectangle
6.6(444): 13-21(odds),27-31(odds),36,41,43
36)8