Lesson 6.6.notebook
October 03, 2016
Before: October 3, 2016
• Can you conclude that the parallelogram is a rhombus, a rectangle, or a square? Explain.
• For what value of x is parallelogram ABCD a rectangle?
• Given WRST is a parallelogram and WS is congruent to RT, how can you classify WRST? Explain.
Sep 23­11:20 AM
During: Trapezoids and Kites
Learning Target: To verify and use properties of trapezoids and kites.
Sep 23­11:20 AM
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Lesson 6.6.notebook
October 03, 2016
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.
Sep 23­11:20 AM
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.
Sep 23­11:20 AM
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Lesson 6.6.notebook
October 03, 2016
Theorem 6 – 19 Sep 23­11:20 AM
Problem 1: Finding Angle Measures in Trapezoids “I Do”
• CDEF is an isosceles trapezoid and m<C = 65. What are m<D, m<E, and m<F?
Sep 23­11:20 AM
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Lesson 6.6.notebook
October 03, 2016
Problem 1: Finding Angle Measures in Trapezoids “We Do”
• In the diagram, PQRS is an isosceles trapezoid and • m<R = 106. What are m<P, m<Q, and m<S?
Sep 23­11:20 AM
Problem 1: Finding Angle Measures in Trapezoids “You Do”
• RSTU is an isosceles trapezoid and m<S = 75. What are m<R, m<T, and m<U?
Sep 23­11:20 AM
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Lesson 6.6.notebook
October 03, 2016
Theorem 6 – 20 Theorem
If...
Then…
If a quadrilateral is an isosceles trapezoid, then its diagonals are congruent.
Sep 23­11:20 AM
• 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
If…
Then…
If a quadrilateral is a trapezoid,
then the midsegment is parallel
to the bases, and the length of the midsegment is half the sum of the lengths of the bases.
Sep 23­11:20 AM
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Lesson 6.6.notebook
October 03, 2016
Problem 2: Using the Midsegments of a Trapezoid “I Do”
• QR is the midsegment of • trapezoid LMNP. What is x?
Sep 23­11:20 AM
Problem 2: Using the Midsegments of a Trapezoid “We Do”
• MN is the midsegment of trapezoid PQRS. What is x? What is MN? Sep 23­11:20 AM
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Lesson 6.6.notebook
October 03, 2016
Problem 2: Using the Midsegments of a Trapezoid “You Do”
• TU is the midsegment of trapezoid WXYZ. What is x?
Sep 23­11:20 AM
• A kite is a quadrilateral with two pairs of consecutive sides congruent and no opposite sides congruent.
Theorem 6 – 22
If....
Then... If a quadrilateral is a kite, then its diagonals are perpendicular.
Sep 23­11:20 AM
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Lesson 6.6.notebook
October 03, 2016
Problem 3: Finding Angle Measures in Kites “I Do”
• Quadrilateral DEFG is a kite. • What are m<1, m<2, and m<3?
Sep 23­11:20 AM
Problem 3: Finding Angle Measures in Kites “We Do”
• Quadrilateral KLMN is a kite. What are m<1, m<2, and m<3?
Sep 23­11:20 AM
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Lesson 6.6.notebook
October 03, 2016
Problem 3: Finding Angle Measures in Kites “You Do”
• Quadrilateral ABCD is a kite. • What are m<1 and m<2?
Sep 23­11:20 AM
Concept Summary: Relationships Among Quadrilaterals
Sep 23­11:20 AM
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Lesson 6.6.notebook
October 03, 2016
After: Lesson Check
• What are the measures of the numbered angles?
• What is the length of the midsegment of a trapezoid with bases of length 14 and 26?
Sep 23­11:20 AM
After: Lesson Check
• Is a kite a parallelogram? Explain.
• How is a kite similar to a rhombus? How is it different? Explain.
• 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.
Sep 23­11:20 AM
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Lesson 6.6.notebook
October 03, 2016
Homework:
Page 394, 7 – 15 all, 16 – 24 even, 28 – 33 all Sep 23­11:20 AM
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