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Geometry

1 of 14. Geometry. Agenda. Chapter 6.3 – Proving quadrilaterals are parallelogram Homework: check the last 2 slides. Theorem 6.7 If both pairs of opposites angles are congruent, then the quadrilateral is a parallelogram. Q. R. S. P. 2 of 14. Theorems about Parallelograms.

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Geometry

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  1. 1 of 14 Geometry Agenda • Chapter 6.3 – Proving quadrilaterals are parallelogram • Homework: check the last 2 slides

  2. Theorem 6.7 If both pairs of opposites angles are congruent, then the quadrilateral is a parallelogram. Q R S P 2 of 14 Theorems about Parallelograms Theorem 6.6 If both pairs of opposites sides are congruent, then the quadrilateral is a parallelogram. Q R S P

  3. Theorem 6.9 If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. Q R M P S 3 of 14 Theorems about Parallelograms Theorem 6.8 If an angle of a quadrilateral is supplementary to both its consecutive angles, then the quadrilateral is a parallelogram. Q R x 180 - x x S P

  4. 4 of 14 Theorems about Parallelograms Theorem 6.10 If one pair of opposite sides of a quadrilateral are congruent and parallel, then the quadrilateral is a parallelogram. B C A D

  5. 5 of 7 Homework A. 1. In parallelogram ABCD, mA=3x+15 and mB=5x-17. Find x. 2. In parallelogram KJLM , JK=10y-5 and LM=-6y+27. Find y.

  6. Chapter 6 – Quadrilaterals 6.3 - Proving Quadrilaterals are Parallelograms Homework B. Show that a(2,-1), B(1,3), C(6,5), and D(7,1) are the vertices of a parallelogram. Method 1: Show that opposite sides have the same slope. Method 2: Show that opposite sides have the same length. Method 3: Show that one pair of opposite sides is congruent and parallel.

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