 6.3 Showing Quadrilaterals are Parallelograms. We can use the theorems from 6.2 to prove that quadrilaterals are parallelograms  What 5 facts are ALWAYS.

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 6.3 Showing Quadrilaterals are Parallelograms

We can use the theorems from 6.2 to prove that quadrilaterals are parallelograms  What 5 facts are ALWAYS true about parallelograms? 1) Both pairs of opposite sides are parallel. 2) Both pairs of opposite sides are congruent. 3) Both pairs of opposite angles are congruent. 4) One angle is supplementary to both of its consecutive angles. 5) Diagonals bisect each other.

Example 1 Tell whether the quadrilateral is a parallelogram. Explain your reasoning.

You Try It…  Tell whether each quadrilateral is a parallelogram. Explain your reasoning.

Example 2  Use the slopes of the segments in the diagram to determine if the quadrilateral is a parallelogram.

You Try It…

Application

6.4  Rhombuses  Rectangles  Squares

Vocabulary

Example 1  A) In the diagram, PQRS is a rhombus. Find QR, RS, and SP.  B) Use the information in the diagram to name the special quadrilateral.

Corollaries Rhombus Corollary: If a quadrilateral has 4 congruent sides, then it is a rhombus. Rectangle Corollary: If a quadrilateral has 4 right angles, then it is a rectangle. Square Corollary: If a quadrilateral has 4 congruent sides and four right angles, then it is a square.

You Try It…  Use the information in the diagram to name the special quadrilateral

Theorems about Diagonals 1) The diagonals of a rhombus are perpendicular. 2) The diagonals of rectangle are congruent.

Example 2

You Try It…