Properties of Parallelograms

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6-2 Properties of Parallelograms

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Presentation transcript:

Properties of Parallelograms Lesson 7.2 Properties of Parallelograms

Essential Question: What are the properties of parallelograms?

Parallelogram A quadrilateral with two pairs of opposite sides that are parallel. Symbol We could write “parallelogram ABCD”. Or, we could use the symbol and write “ ABCD”. Or, “Pgram ABCD”.

Theorem 7.3 Parallelogram Opposite Sides Theorem In a parallelogram, opposite sides are congruent.

Example 1 Solve for x and y. 4x + 10 = 42 4x = 32 x = 8 2y – 12 = 20 2y = 32 y=16

Theorem 7.4 Parallelogram Opposite Angles Theorem In a parallelogram, the opposite angles are congruent.

Find the values of x and y. Example 2 Find the values of x and y. 2x = 50 x = 25 y + 3 = 18 y= 15

Theorem 7.5 Parallelogram Consecutive Angles Theorem In a parallelogram, consecutive angles are supplementary.

Example 3 Solve for x. 3x + 120 = 180 3x = 60 x = 20

7.6 Parallelogram Diagonals Theorem The diagonals of a parallelogram bisect each other.

Application Solve for x. 5x – 8 = 2x + 10 5x = 2x + 18 3x = 18 x = 6

These properties must be memorized. In a Parallelogram… Opposite sides are parallel. Opposite sides are congruent. Opposite angles are congruent. Consecutive angles are supplementary. Diagonals bisect each other. These properties must be memorized. November 27, 2018November 27, 2018

Write a two-column proof. Given ABCD and GDEF are parallelograms Prove Statements_______________ Reasons_____________ 1. Given ABCD and GDEF are parallelograms 2. Parallelogram Opp Angles Theorem 2. 3. 3. Vertical Angles Thm 4. Transitive Prop. 4.