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5-Minute Check 1

5-Minute Check 1. 1) LMNO is a rhombus. Find x. 2) LMNO is a rhombus. Find y. 3) QRST is a square. Find n if m TQR = 8 n + 8. 6-6 Trapezoids and Kites. Trapezoid. Quadrilateral with one pair of parallel sides Parallel sides are called the “bases ”.

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5-Minute Check 1

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  1. 5-Minute Check 1 1) LMNO is a rhombus. Find x. 2) LMNO is a rhombus. Find y. 3) QRST is a square. Find n if mTQR = 8n + 8.

  2. 6-6 Trapezoids and Kites

  3. Trapezoid • Quadrilateral with one pair of parallel sides • Parallel sides are called the “bases”. • Non-parallel sides are called the “legs”.

  4. Isosceles Trapezoid • Trapezoid where the legs are congruent • Diagonals are congruent.

  5. Theorem • Base angles of an isosceles trapezoid are congruent. • What else can you tell me about angles x and y? • They are supplements! y y x x

  6. TOO: Find the missing angles 1) 2) 110 110 70 70 145 145 35 35

  7. Theorem • The median of a trapezoid is • parallel to the bases • (Base + Base) divided by 2 b m b

  8. Example: EF is the median of Trapezoid ABCD • If AB = 25 and DC = 13, find EF. • If AB = 29 and EF = 24, find DC. TOO: If AB = 7y + 6, EF = 5y – 3, and DC = y – 5, find y and EF. (both answers are decimals!!) 19 19 D C E F A B 3.5 14.5

  9. Kite Is a Quadrilateral Diagonals are Perpendicular 2 consecutive sets of sides are congruent Longer diagonal bisects the Angles and the shorter diagonal.

  10. Example If MNPQ is a kite, find NP. NR2 + MR2 = MN2 Pythagorean Theorem (6)2 + (8)2 = MN2 36 + 64 = MN2 100 = MN2 10 = MN Since MN  NP, NP = 10.

  11. Example If BCDE is a kite, find mCDE. A. 28° B. 36° C. 42° D. 55°

  12. Homework • Pg. 444 #8-11, 16-27, 41-44

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