Lesson 7.2 Properties of Parallelograms Learning

Transcript:Lesson 7.2 Properties of Parallelograms Learning:
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 Plan in 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