1. Lesson 5-5: Trapezoids (page 190)
Essential Question
How can the properties of quadrilaterals be used to solve real life problems?

2. a quadrilateral with exactly one pair of parallel sides.
TRAPEZOID:
a quadrilateral with exactly one pair of parallel sides.
BASES of a TRAPEZOID : the parallel sides.
LEGS of a TRAPEZOID : the non-parallel sides.
base ➤
leg
leg ➤
base

3. Trapezoid
leg ➤
base ➤
base
leg

4. ISOSCELES TRAPEZOID: a trapezoid with congruent legs.➤ ➤

5. Base angles of an isosceles trapezoid are congruent .
Theorem 5-18
Base angles of an isosceles trapezoid are congruent . B ➤ A ➤ X Y
Proof: For an outline of this proof see page 190.
Note that parallelograms are used in the proof.

6. Review: Median of a Triangle Median of a Trapezoid
MEDIAN of a TRAPEZOID: is the segment that joins
the midpoints of the legs. ● ● ●
Review:
Median of a Triangle
Median of a Trapezoid

7. Theorem 5-19
The median of a trapezoid: (1) is parallel to the bases; (2) has a length equal to the average of the base lengths.
Given: Trapezoid PQRS with median MN
Prove: S R M N P Q
Proof: For an outline of this proof see page Note congruent triangles are used in the proof.

8. Theorem 5-19
The median of a trapezoid: (1) is parallel to the bases; (2) has a length equal to the average of the base lengths.
Given: Trapezoid PQRS with median MN
Prove: S ➤ R ➤ M N ➤ P Q
Proof: For an outline of this proof see page Note congruent triangles are used in the proof.

9. Theorem 5-19
The median of a trapezoid: (1) is parallel to the bases; (2) has a length equal to the average of the base lengths.
Given: Trapezoid PQRS with median MN
Prove: S ➤ R ➤ M N ➤ P Q
Proof: For an outline of this proof see page Note congruent triangles are used in the proof.

10. Example #1: Given a trapezoid and its median, find the value of “x”.6 x 12

11. Example #2: Given a trapezoid and its median, find the value of “x”.

12. The QUADRILATERAL Hierarchy
Parallelogram
Trapezoid
Rhombus
Rectangle
Isosceles
Trapezoid
Square

13. CHARACTERISTICS Both pairs off opposite sides are parallel
Parallel- ogram
Rectangle
Rhombus
Square
Trapezoid
Isosceles Trapezoid
Both pairs off opposite sides are parallel
Diagonals are congruent
Both pairs off opposite sides are congruent
At least one right angle
Both pairs off opposite angles are congruent
Exactly one pair of opposite sides are parallel
Diagonals perpendicular
Consecutive sides are congruent
Consecutive angles are congruent
Diagonals bisect each other
Diagonals bisect opposite angles

14. X supp CHARACTERISTICS Both pairs off opposite sides are parallel
Parallel- ogram
Rectangle
Rhombus
Square
Trapezoid
Isosceles Trapezoid
Both pairs off opposite sides are parallel X
Diagonals are congruent
Both pairs off opposite sides are congruent
At least one right angle
Both pairs off opposite angles are congruent
Exactly one pair of opposite sides are parallel
Diagonals perpendicular
Consecutive sides are congruent
Consecutive angles are congruent
supp
Diagonals bisect each other
Diagonals bisect opposite angles

15. X supp CHARACTERISTICS Both pairs off opposite sides are parallel
Parallel- ogram
Rectangle
Rhombus
Square
Trapezoid
Isosceles Trapezoid
Both pairs off opposite sides are parallel X
Diagonals are congruent
Both pairs off opposite sides are congruent
At least one right angle
Both pairs off opposite angles are congruent
Exactly one pair of opposite sides are parallel
Diagonals perpendicular
Consecutive sides are congruent
Consecutive angles are congruent
supp
Diagonals bisect each other
Diagonals bisect opposite angles

16. X supp CHARACTERISTICS Both pairs off opposite sides are parallel
Parallel- ogram
Rectangle
Rhombus
Square
Trapezoid
Isosceles Trapezoid
Both pairs off opposite sides are parallel X
Diagonals are congruent
Both pairs off opposite sides are congruent
At least one right angle
Both pairs off opposite angles are congruent
Exactly one pair of opposite sides are parallel
Diagonals perpendicular
Consecutive sides are congruent
Consecutive angles are congruent
supp
Diagonals bisect each other
Diagonals bisect opposite angles

17. X supp CHARACTERISTICS Both pairs off opposite sides are parallel
Parallel- ogram
Rectangle
Rhombus
Square
Trapezoid
Isosceles Trapezoid
Both pairs off opposite sides are parallel X
Diagonals are congruent
Both pairs off opposite sides are congruent
At least one right angle
Both pairs off opposite angles are congruent
Exactly one pair of opposite sides are parallel
Diagonals perpendicular
Consecutive sides are congruent
Consecutive angles are congruent
supp
Diagonals bisect each other
Diagonals bisect opposite angles

18. X supp CHARACTERISTICS Both pairs off opposite sides are parallel
Parallel- ogram
Rectangle
Rhombus
Square
Trapezoid
Isosceles Trapezoid
Both pairs off opposite sides are parallel X
Diagonals are congruent
Both pairs off opposite sides are congruent
At least one right angle
Both pairs of opposite angles are congruent
Exactly one pair of opposite sides are parallel
Diagonals perpendicular
Consecutive sides are congruent
Consecutive angles are congruent
supp
Diagonals bisect each other
Diagonals bisect opposite angles

19. X supp CHARACTERISTICS Both pairs off opposite sides are parallel
Parallel- ogram
Rectangle
Rhombus
Square
Trapezoid
Isosceles Trapezoid
Both pairs off opposite sides are parallel X
Diagonals are congruent
Both pairs off opposite sides are congruent
At least one right angle
Both pairs off opposite angles are congruent
Exactly one pair of opposite sides are parallel
Diagonals perpendicular
Consecutive sides are congruent
Consecutive angles are congruent
supp
Diagonals bisect each other
Diagonals bisect opposite angles

20. Activity with cutting out shapes.
Check out the tangram calendars and websites!
Rearrange the 7 pieces back into a SQUARE.
How can the properties of quadrilaterals be used to solve real life problems?

21. The tangrams can form 13 convex polygons! 1 triangle 6 quadrilaterals
2 pentagons
4 hexagons
Rearrange the 7 pieces into a TRIANGLE.
Rearrange the 7 pieces into a RECTANGLE.
Rearrange the 7 pieces into a TRAPEZOID.
Rearrange the 7 pieces into a PARALLELOGRAM.

22. Assignment
Written Exercises on pages 192 & 193
RCOMMENDED: 1 to 9 odd numbers
REQUIRED: 11 to 16 ALL numbers,
26 (NO Proof)
Prepare for Quiz on Lessons 5-4 & 5-5
Tangrams Picture Project
Worth 20 points PLUS possible bonus!
All pictures will be judged to earn
the possible bonus points.
How can the properties of quadrilaterals be used to solve real life problems?

23. Written Exercises on page 193 What is your conclusion?
CLASS Assignment
Written Exercises on page 193
17 to 20 ALL numbers
What is your conclusion?
21 to 25 ALL numbers & 29
How can the properties of quadrilaterals be used to solve real life problems?
Continue

24. Prepare for Quiz on Lessons 5-4 & 5-5
Prepare for Test on
Chapter 5: Quadrilaterals
Tangrams Picture Project
Worth 20 points PLUS possible bonus!
All pictures will be judged to earn
the possible bonus points.
How can the properties of quadrilaterals be used to solve real life problems?