Lesson 7.2 Properties of Parallelograms Learning

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Lesson 7.2 Properties of Parallelograms Learning

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Lesson 7.2 Properties of Parallelograms Learning Target: Prove and use properties of parallelograms. Success Criteria: I can prove properties of parallelograms. I can use properties of parallelograms. I can solve problems involving

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Lesson 7.2 Properties of Parallelograms

Learning Target:
Prove and use properties of parallelograms. Success Criteria:
I can prove properties of parallelograms.
I can use properties of parallelograms.
I can solve problems involving parallelograms in the coordinate plane.

Vocabulary
parallelogram, p. 362

Parallelogram Opposite Sides Theorem

Parallelogram Opposite Sides Theorem Planin Action

Example 1 Using Properties of Parallelograms Find the values of x and y. ABCD is a parallelogram by the definition of a parallelogram.
Use the Parallelogram Opposite Sides Theorem to find the
value of x. Opposite sides of a parallelogram are congruent. Subtract 4 from each side. SOLUTION

Parallelogram Diagonals Theorem

Example 2 Using Properties of a Parallelogram SOLUTION

Example 3 Writing a Two-Column Proof Write a two-column proof. Given ABCD and GDEF are parallelograms. 1. ABCD and GDEF are parallelograms. 1. Given 2. Parallelogram Opposite Angles Theorem 3. Vertical Angles Congruence Theorem 4. Transitive Property of Angle Congruence STATEMENTS REASONS

Example 4 Using Parallelograms in the Coordinate Plane Find the coordinates of the intersection of the diagonals of ▱LMNO
with vertices L(1, 4), M(7, 4), N(6, 0), and O(0, 0). Midpoint Formula SOLUTION Check Graph ▱LMNO
and draw the diagonals. ✓

Example 5 Using Parallelograms in the Coordinate Plane Step 2 Step 3 Step 1 Graph the vertices W, X, and Z. SOLUTION So, the coordinates of vertex Y are (2, 1). 5 5 Y

Example 5 Using Parallelograms in the Coordinate Plane So, the coordinates of vertex Y are (2, 1). Step 3

Lesson 7.2 Properties of Parallelograms Learning

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