6-2 Properties of Parallelograms Using the definition of parallelogram, students will construct several theorems regarding the equivalence of sides, angles, and bisection of diagonals. To use relationships among sides and among angles of parallelograms To use relationships involving diagonals of parallelograms.

Example 1: Using Consecutive Angles

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Key Concepts

Proof of Theorem 6-2

Example 2: Using Algebra

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Key Concepts

Proof of Theorem 6-3

Example 3: Using Algebra

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Key Concepts

Example 4: Real-World Connection

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The following questions are designed to help you determine if you personally understood today’s lesson. Please be sure to record the number you get right on your portfolio sheet. Be sure to take time to understand the ones you miss! 6-2 Quiz

1. LMNO is a parallelogram 1. LMNO is a parallelogram. If NM = x + 15 and OL = 3x + 5 find the value of x and then find NM and OL. x = 7, NM = 20, OL = 22 x = 5, NM = 20, OL = 20 x = 7, NM = 22, OL = 22 x = 5, NM = 22, OL = 20 Non-Response Grid

2. Find the values of the variables in the parallelogram 2. Find the values of the variables in the parallelogram. The diagram is not to scale. x = 49; y = 29; z = 102 x = 29; y = 49; z = 131 x = 49; y = 49; z = 131 x = 29; y = 49; z = 102 Non-Response Grid

  119 61 129 68 Non-Response Grid

  9 12 6 3 Non-Response Grid

5. Find AM in the parallelogram if PN =9 and AO = 4 5. Find AM in the parallelogram if PN =9 and AO = 4. The diagram is not to scale. 8 4 9 4.5 Non-Response Grid

Assignment 6-2 p.297-301 #2- 52 even