Warm up:1. Can you conclude that the parallelogram is a rhombus,

a rectangle, or a square? Explain.

2. For what value of x is parallelogram ABCD a rectangle?

3. Given WRST is a parallelogram and WS is congruent to RT, how can you classify WRST? Explain.

6.6/6.7 - TRAPEZOIDS AND KITESAND

POLYGONS IN THE COORDINATE PLANE

I can verify and use properties of trapezoids and kites. I can classify polygons in the coordinate plane.

Trapezoids• A trapezoid is a quadrilateral with exactly one pair of

parallel sides. The parallel sides of a 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.

Isosceles Trapezoid• 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.

Theorem 6 – 19 Theorem 6 – 19

Theorem If… Then…

If a quadrilateral is an isosceles

trapezoid, then each pair of base

angles is congruent.

Problem: Finding Angle Measures in Trapezoids• CDEF is an isosceles trapezoid and m<C = 65. What are

m<D, m<E, and m<F?

Problem: Finding Angle Measures in Trapezoids• In the diagram, PQRS is an isosceles trapezoid and

m<R = 106. What are m<P, m<Q, and m<S?

Problem: Finding Angle Measures in Trapezoids • RSTU is an isosceles trapezoid and m<S = 75. What are

m<R, m<T, and m<U?

Theorem 6 – 20 Theorem 6 – 20

Theorem If… Then…

If a quadrilateral is an isosceles

trapezoid, then its diagonals are

congruent.

• In Chapter 5 – 1, we learned about midsegments of triangles. 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.Trapezoid Midsegment Theorem

Theorem If… Then…

If a quadrilateral is a trapezoid, then

1. The midsegment is parallel to the bases, and

2. The length of the midsegment is half

the sum of the lengths of the

bases.

Problem: Using the Midsegments of a Trapezoid• QR is the midsegment of trapezoid LMNP. What is x?

Problem: Using the Midsegments of a Trapezoid• MN is the midsegment of trapezoid PQRS. What is x?

What is MN?

Problem: Using the Midsegments of a Trapezoid• TU is the midsegment of trapezoid WXYZ. What is x?

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

• The angles, sides, and diagonals of a kite have certain properties.

Theorem 6 – 22

Theorem If… Then…

If a quadrilateral is a kite, then its diagonals are perpendicular.

Problem: Finding Angle Measures in Kites

• Quadrilateral DEFG is a kite. What are m<1, m<2, and m<3?

Problem: Finding Angle Measures in Kites

• Quadrilateral KLMN is a kite. What are m<1, m<2, and m<3?

Problem: Finding Angle Measures in Kites

• Quadrilateral ABCD is a kite. What are m<1 and m<2?

Concept Summary: Relationships Among Quadrilaterals

After: Lesson Check

1. What are the measures of the numbered angles?

2. What is the length of the midsegment of a trapezoid with bases of length 14 and 26?

After: Lesson Check

3. Is a kite a parallelogram? Explain.

4. How is a kite similar to a rhombus? How is it different? Explain.

5. Since a parallelogram has two pairs of parallel sides, it certainly has one pair of parallel sides. Therefore, a parallelogram must also be a trapezoid. What is the error in this reasoning? Explain.

HOMEWORK:Page 394, #8-34 even

AND

Page 403, #5-7 all, 10