Geometry 6.3 I can recognize the conditions that ensure a quadrilateral is a parallelogram.

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6.3 Proving that a Quadrilateral is a Parallelogram

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Presentation transcript:

Geometry 6.3 I can recognize the conditions that ensure a quadrilateral is a parallelogram.

Tests for Parallelograms If both pairs of opposite sides are parallel, then it’s a parallelogram. If both pairs of opposite sides are congruent, then it’s a parallelogram. If both pairs of opposite angles are congruent, then it’s a parallelogram. If diagonals bisect each other, then it’s a parallelogram. If ONE pair of opposite sides are both parallel and congruent, then it’s a parallelogram.

Are the following quadrilaterals parallelograms? _____ Why or Why not?______________________________ A quadrilateral is a parallelogram if any one of the following is true. If both pairs of opposite sides are parallel, then it’s a parallelogram. If both pairs of opposite sides are congruent, then it’s a parallelogram. If both pairs of opposite angles are congruent, then it’s a parallelogram. If diagonals bisect each other, then it’s a parallelogram. If ONE pair of opposite sides are both parallel and congruent, then it’s a parallelogram. YES

Are the following quadrilaterals parallelograms? _____ Why or Why not?______________________________ A quadrilateral is a parallelogram if any one of the following is true. If both pairs of opposite sides are parallel, then it’s a parallelogram. If both pairs of opposite sides are congruent, then it’s a parallelogram. If both pairs of opposite angles are congruent, then it’s a parallelogram. If diagonals bisect each other, then it’s a parallelogram. If ONE pair of opposite sides are both parallel and congruent, then it’s a parallelogram. YES YES, alternate interior angles are equal so the top and bottom are also parallel.

Are the following quadrilaterals parallelograms? _____ Why or Why not?______________________________ A quadrilateral is a parallelogram if any one of the following is true. If both pairs of opposite sides are parallel, then it’s a parallelogram. If both pairs of opposite sides are congruent, then it’s a parallelogram. If both pairs of opposite angles are congruent, then it’s a parallelogram. If diagonals bisect each other, then it’s a parallelogram. If ONE pair of opposite sides are both parallel and congruent, then it’s a parallelogram. NO NO, Top and Bottom would need to be BOTH parallel and congruent.

Are the following quadrilaterals parallelograms? _____ Why or Why not?______________________________ A quadrilateral is a parallelogram if any one of the following is true. If both pairs of opposite sides are parallel, then it’s a parallelogram. If both pairs of opposite sides are congruent, then it’s a parallelogram. If both pairs of opposite angles are congruent, then it’s a parallelogram. If diagonals bisect each other, then it’s a parallelogram. If ONE pair of opposite sides are both parallel and congruent, then it’s a parallelogram. YES Yes, Corresponding angles are equal so lines are parallel.

Find the values x and y that ensure each quadrilateral is a parallelogram. 4y 6y - 42

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

Quadrilateral GHJK has vertices G(-2,4), H(4,2), J(4,-2) and K(-2,-1). Determine whether GHJK is a parallelogram by using the following theorem: One pair of opposite sides are both parallel and congruent. Use slopes to determine if a pair of sides are parallel. (Same Slopes means the sides are parallel.) Use distance formula or Pythagorean theorem to show if the sides congruent. Since opposite sides have the same slope they are parallel. Since opposite sides are the same length they are congruent. Thus GHJK must be a parallelogram.

Homework 6.3 Pg. 337 #9-14, 20-25, 41-44, 45