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Warm up…

Warm up…. Page 318 #’s 64 – 76. Happy Friday. 6.5. SWBAT…. To verify and use properties of trapezoids and kites. Properties of a Trapezoid. Exactly one pair of parallel sides Parallel sides called bases non-parallel sides called legs Base angles formed by the base and one of the legs

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Warm up…

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  1. Warm up… • Page 318 #’s 64 – 76 Happy Friday

  2. 6.5

  3. SWBAT… • To verify and use properties of trapezoids and kites.

  4. Properties of a Trapezoid • Exactly one pair of parallel sides • Parallel sides called bases • non-parallel sides called legs • Base angles formed by the base and one of the legs • If the legs are congruent then the trapezoid is an isosceles trapezoid.

  5. Theorems • Both pairs of base angles of an isosceles trapezoid are congruent • The diagonals of an isosceles trapezoid are congruent.

  6. Example 1 • Finish the flow proof. • Given: MNOP is an isosceles trapezoid • Prove: MO congruent to NP

  7. Given: MNOP is an isosceles trapezoidProve: MO congruent to NP N M O P MNOP is an isosceles trapezoid MP = NO Def of isosc trap GIVEN <MPO = <NOP Base <‘s = SAS MO = NP CPCTC PO = PO Reflexive

  8. Example 2 • ABCD is a quadrilateral with vertices A (5, 1), B (-3, -1), C (-2, 3) and D (2, 4). a. Verify that ABCD is a trapezoid. b. Determine whether ABCD is an isosceles trapezoid. Explain.

  9. Medians • The segment that joins midpoints of the legs of a trapezoid is the median. (sometimes called the midsegment) • The median of a trapezoid is parallel to the bases and its measure is one-half the sum of the bases. A B M MN= ½(AB + CD) N C D

  10. Example 3 • DEFG is an isosceles trapezoid with median MN. • Find DG if EF = 20 and MN = 30 • Find <1, <2, <3 and <4 if <1 = 3x + 5 and <3 = 6x – 5

  11. Kites • A quadrilateral with two pairs of adjacent sides congruent and no opposite sides congruent. • Diagonals of a kites are perpendicular

  12. Example 4 • Find m<1, m<2, m<3 in the kite. S 1 T R 3 2 72 U

  13. CLASSWORK… • Page 322-323 #’s 1-18

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