1. Trapezoids and Kites

2. Trapezoids and Kites
A trapezoid is a quadrilateral with exactly one pair of parallel sides.
The parallel sides are of trapezoid are called bases.
The nonparallel sides are called legs.
The two angles that share a base of a trapezoid are called base angles. A trapezoid has two pairs of base angles.

3. Trapezoids and Kites
An isosceles trapezoid is a trapezoid with legs that are congruent. ABCD below is an isosceles trapezoid. The angles of an isosceles trapezoid have some unique properties.

4. Trapezoids and Kites

5. Trapezoids and Kites

6. Trapezoids and Kites Problem 1:
CDEF is an isosceles trapezoid and m<C = 65. What are m<D, m<E, and m<F?

7. Trapezoids and Kites Problem 1b:
PQRS is an isosceles trapezoid and m<R = What are m<P, m<Q, and m<S?

8. Trapezoids and Kites Problem 2:
The second ring of the paper fan consists of 20 congruent isosceles trapezoids that appear to form circles. What are the measures of the base angles of these trapezoids?

9. Find the measures of the numbered angles in each isosceles trapezoid.
Trapezoids and Kites
Problem 3:
Find the measures of the numbered angles in each isosceles trapezoid.

10. Find the measures of the numbered angles in each isosceles trapezoid.
Trapezoids and Kites
Problem 3b:
Find the measures of the numbered angles in each isosceles trapezoid.

11. Find the measures of the numbered angles in each isosceles trapezoid.
Trapezoids and Kites
Problem 3c:
Find the measures of the numbered angles in each isosceles trapezoid.

12. Trapezoids also have midsegments.
Trapezoids and Kites
In lesson 5.1 you learned about the midsegments of triangles…What are they????
Trapezoids also have midsegments.
The midsegment of a trapezoid is the segment that joins the midpoints of its legs. The midsegment has two unique properties.

13. Trapezoids and Kites

14. Problem 4: Segment QR is the midsegment of trapezoid LMNP. What is x?
Trapezoids and Kites
Problem 4:
Segment QR is the midsegment of trapezoid LMNP. What is x?

15. Problem 4b: Find EF is the trapezoid.
Trapezoids and Kites
Problem 4b:
Find EF is the trapezoid.

16. Problem 4c: Find EF is the trapezoid.
Trapezoids and Kites
Problem 4c:
Find EF is the trapezoid.

17. Find the lengths of the segments with variable expressions.
Trapezoids and Kites
Problem 4e:
Find the lengths of the segments with variable expressions.

18. Trapezoids and Kites
A kite is a quadrilateral with two pairs of consecutive sides congruent and no opposite sides congruent.

19. Trapezoids and Kites

20. Quadrilateral DEFG is a kite. What are m<1, m<2, m<3?
Trapezoids and Kites
Problem 5:
Quadrilateral DEFG is a kite. What are m<1, m<2, m<3?

21. Section 6.6 – Trapezoids and Kites
Problem 5b:
Find the measures of the numbered angles in each kite.

22. Problem 5c: Find the measures of the numbered angles in each kite.
Trapezoids and Kites
Problem 5c:
Find the measures of the numbered angles in each kite.

23. Problem 5d: Find the measures of the numbered angles in each kite.
Trapezoids and Kites
Problem 5d:
Find the measures of the numbered angles in each kite.

24. Problem 5e: Find the value(s) of the variable(s) in each kite.
Trapezoids and Kites
Problem 5e:
Find the value(s) of the variable(s) in each kite.

25. Problem 5f: Find the value(s) of the variable(s) in each kite.
Trapezoids and Kites
Problem 5f:
Find the value(s) of the variable(s) in each kite.

26. Section 6.6 – Trapezoids and Kites

27. Trapezoids and Kites Problem 6:
Determine whether each statement is true or false. Be able to justify your answer.
All squares are rectangles
A trapezoid is a parallelogram
A rhombus can be a kite
Some parallelograms are squares
Every quadrilateral is a parallelogram
All rhombuses are squares.

28. Trapezoids and Kites Problem 7:
Name each type of quadrilateral that can meet the given condition.
Exactly one pair of congruent sides
Two pairs of parallel sides
Four right angles
Adjacent sides that are congruent
Perpendicular diagonals
Congruent diagonals

29. Trapezoids and Kites Problem 8:
Can two angles of a kite be as follows? Explain!
Opposite and acute
Consecutive and obtuse
Opposite and supplementary
Consecutive and supplementary
Opposite and complementary
Consecutive and complementary

30. Trapezoids and Kites Problem 8:
Can two angles of a kite be as follows? Explain!
Opposite and acute
Consecutive and obtuse
Opposite and supplementary
Consecutive and supplementary
Opposite and complementary
Consecutive and complementary

31. Trapezoids and Kites