6-2B Proving Quadrilaterals Are Parallelograms

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Objective: Prove that a given quadrilateral is a parallelogram. 6.3 Proving Quadrilaterals are Parallelograms Handbook, p. 19.

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Presentation transcript:

6-2B Proving Quadrilaterals Are Parallelograms How do you show that a quadrilateral is a parallelogram? What are the conditions?

Properties of Parallelograms The opposite sides of a parallelogram are parallel (by definition). The opposite angles of a parallelogram are congruent. The opposite sides of a parallelogram are congruent. The consecutive angles of a parallelogram are supplementary. The diagonals of a parallelogram bisect each other.

Write the Converse of the definition The opposite sides of a parallelogram are parallel (by definition). A quadrilateral is a parallelogram if both pairs of opposite sides are parallel (definition). Draw a parallelogram on a piece of graph paper. How do you check for 2 pairs of parallel sides?

Write the converse of: The opposite angles of a parallelogram are congruent. If both pairs of angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram. 1. Measure the angles of your parallelogram.

Write the Converse of The opposite sides of a parallelogram are congruent. If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. 1. Measure the length of the sides of your quadrilateral. Write down the measurements.

Write the Converse of The consecutive angles of a parallelogram are supplementary. If the consecutive angles of a quadrilateral are supplementary, then the quadrilateral is a parallelogram. 1. Add up the measures of the consecutive angles. Are they supplementary?

Write the Converse of The diagonals of a parallelogram bisect each other. If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. Draw diagonals in your quadrilateral. Measure the diagonals. Measure each part of the diagonals and write down the measurement.

Is the quadrilateral a parallelogram? Yes, diagonals bisect each other. Yes, Opposite sides are congruent. 70° 110° ?? The congruent sides may not be parallel. Yes, consecutive angles are supplementary.

Conditions for a Parallelogram A quadrilateral is a parallelogram if both pairs of opposite sides are parallel (definition). If both pairs of angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram. If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. If the consecutive angles of a quadrilateral are supplementary, then the quadrilateral is a parallelogram. If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

Assignment 6-2B Page 425, 1-12, 25-28