Post on 22-Dec-2015
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• MN is the midsegment of trapezoid PQRS. What is x?
What is MN?
• 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?
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.