1. Trapezoids and Kites
Geometry 6-5

2. Recall the shape of a toy kite
Recall the shape of a toy kite. What definition would you write to describe the shape in geometric terms?
Kite Investigation

3. Kite Investigation Kite Definition
A kite is a quadrilateral that has two pairs of consecutive congruent sides, but the opposite sides are not congruent
Kite Investigation

4. Get your supplies
Straight Edge
Patty Paper
Kite Investigation

5. On a piece of patty paper, draw two line segments of different length
Kite Investigation

6. Fold the paper, so that the endpoints are exactly on the fold
Kite Investigation

7. Trace the first two segments through the patty paper
Kite Investigation

8. Kite Investigation Unfold the paper and label your kite G,L,A,D L G A

9. Kite Investigation Measure each of the four angles
What conclusions can you draw? L G A D
Kite Investigation

10. Kite Angles Conjecture
The non-vertex angles of a kite are congruent
Kite Angles Conjecture

11. Kite Investigation Add the diagonals into your diagram
Label the intersecting point M L G M A D
Kite Investigation

12. Kite Investigation Measure the angles at point M
What can you conclude about the diagonals? L G M A D
Kite Investigation

13. Kite Diagonals Conjecture
The diagonals of a kite are perpendicular
Kite Diagonals Conjecture

14. Measure LM and MD
What can you conclude? L G M A D
Kite Investigation

15. Kite Diagonal Bisector Conjecture
The diagonal connecting the vertex angles of a kite is the perpendicular bisector of the other diagonal
Kite Diagonal Bisector Conjecture

16. Kite Investigation Fold along the diagonals
Does either diagonal bisect any angles? L G M A D
Kite Investigation

17. Kite Angle Bisector Theorem
The vertex angles of a kite are bisected by a diagonal
Kite Angle Bisector Theorem

18. Schedule Quiz on Tuesday / Wednesday 4 questions Classifying
Parallelograms
Proving Parallelograms
Rhombus / Rectangle / Square
Schedule

19. Trapezoid Definition Trapezoid Definition
A trapezoid is a quadrilateral with exactly one pair of parallel sides
Trapezoid Definition

20. Trapezoid Vocabulary Trapezoid Definitions
The parallel sides are called bases
A pair of angles that share a base are called base angles A&B, C&D A B C D
Trapezoid Vocabulary

21. Trapezoid Consecutive Angles Theorem
The consecutive angles between the bases of a trapezoid are supplementary
Trapezoid Consecutive Angles Theorem

22. Trapezoid Investigation
Isosceles Trapezoid
An isosceles trapezoid has congruent legs A B C D
Trapezoid Investigation

23. Trapezoid Investigation
Get your supplies
Protractor
Straight Edge - Ruler
Paper
Compass
Trapezoid Investigation

24. Trapezoid Investigation
Draw two parallel lines – at least two inches apart
Use a compass to create two equal length legs
Label the vertices L,I,O,N L I O N
Trapezoid Investigation

25. Trapezoid Investigation
Measure each pair of base angles
angle L = ?
angle I = ?
angle O= ?
angle N = ? L I O N
Trapezoid Investigation

26. Trapezoid Investigation
What can you conclude about the base angles in an isosceles trapezoid? L I O N
Trapezoid Investigation

27. Isosceles Trapezoid Theorem
The base angles of an isosceles trapezoid are congruent
Isosceles Trapezoid Theorem

28. Trapezoid Investigation
Add the diagonals of the isosceles trapezoid L I O N
Trapezoid Investigation

29. Trapezoid Investigation
Compare the lengths of the two diagonals
What conclusion can we make? L I O N
Trapezoid Investigation

30. Isosceles Trapezoid Diagonals Theorem
The diagonals of an isosceles trapezoid are congruent
Isosceles Trapezoid Diagonals Theorem

31. Practice Problems

32. 53°
127°
127°
Practice Problems

33. DF=10
Angle C=85°
Angle D=95°
Angle F=85°
Practice Problems

34. a = 129.5°
h = 129.5°
Practice Problems

35. a = 118°
t = 43°
Practice Problems

36. 90°
48°
Practice Problems

37. Pages 322 – 325
2-16 even, 22-24, 27,28,32-37, 56
Homework