1. Use Properties of Trapezoids and Kites
Chapter 8.5

2. Trapezoids Trapezoids are quadrilaterals that have 2 parallel sides
The parallel sides are called the bases.
A trapezoid has 1 pair of base angles.
The non-parallel sides are called the legs.
base
Leg
Leg
base

3. Is it a trapezoid? Are the bases parallel?
Find the slope of each base.
If the slopes are the same, then it is a trapezoid.

4. Isosceles Trapezoids
Isosceles triangles have 2 congruent sides with 2 pairs of congruent angles.
The diagonals of an isosceles trapezoid are also congruent.

6. If it is Isosceles find the missing angles.
53º
127º
127º
Because it is an isosceles trapezoid, the base angles are congruent.
Therefore m <A = m <B, and m <D = m <C
Angle A and Angle D are supplementary.
180 – 53 = 127

7. Find the missing angles if it is an Isosceles Trapezoid.
83º
97º
83º

8. Midsegments A midsegment is a segment that connects 2 midpoints.
The midsegment of a trapezoid connects the midpoints of the legs.

10. Find the length of the midsegment

11. Things always have to be more difficult
19.5
5x + 3

12. Find x 45
52.5
10x + 15

13. Page 546, #3 – 15,

14. Kites
A kite is a quadrilateral with 2 pairs of congruent sides, but the opposite sides are not congruent.

16. Diagonals
If the diagonals of a kite are perpendicular, then what shape is created by the diagonals?
If we are given these side lengths, can we find the missing sides XY, WX, YZ , and WZ?

17. Find XY, ZY, WX, and WZ
2√13
6√5

18. Find XY, YZ, WZ, and WX
5√5
√461

19. The figure below is a kite, find the missing angles
What is the sum of the interior angles of a kite?
360
mó E + mó G = 360
140 + mó E + mó G = 360
mó E + mó G = 220
What do we know about the measures of the angles E and G?
They are congruent!

20. Find the missing angles
What do we know about the measures of the angles F and H?
They are congruent!
110º
mó G = 360
80º
280 + mó G = 360
mó G = 80

21. Find the missing angles
mó F + mó G = 360
240 + mó F + mó G = 360
mó F + mó G = 120
mó F = mó G