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Warm - up

Warm - up. In ∆ABC ∠A = 62, ∠B = 58, and ∠C = 60, List the sides from Longest to shortest. In ∆ABC AB = 10, BC = 6, and AC = 15, List the angles from smallest to largest.

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Warm - up

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  1. Warm - up • In ∆ABC ∠A = 62, ∠B = 58, and ∠C = 60, List the sides from Longest to shortest. • In ∆ABC AB = 10, BC = 6, and AC = 15, List the angles from smallest to largest. • A ladder is leaning against a house. The angle made with the ground is 64°. The ladder is 15 feet long. How far up the house does the ladder reach? • A cable is attached to a pole. The cable is 10 feet from the pole and the angle the cable makes with the ground is 78°. How long is the cable? • What are your trigonometric ratios?

  2. Tests for Parallelograms Parallelogram Sec: 6.3 Sol: G.9

  3. Proving Parallelograms Theorem 8.9 : If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. Theorem 8.10 : If both pairs of opposite angles are congruent, then the quadrilateral is a parallelogram.

  4. Theorem 8.11 : If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. Theorem 8.12 : If one pair of opposite sides of a quadrilateral are parallel and congruent, then the quadrilateral is a parallelogram.

  5. Summary – Tests for Parallelograms • Both pairs of opposite sides are parallel (Definition) • Both pairs of opposite sides are congruent (Thm 8.9) • Both pairs of opposite angles are congruent (Thm 8.10) • Diagonal bisect each other (Thm 8.11) • A pair of opposite sides are both parallel and congruent (thm 8.12)

  6. Find the values of x and y the ensure each quadrilateral is a parallelogram

  7. Example: Solve for x and y. 2y+12 x Y 5x - 28 5y

  8. Suggested assignments Classwork: Workbook pg 155-156 1-5, 9-12 Homework: Pg 372-373 7-16, 22, 23 Quadrilateral Parallelogram

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