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GOAL 1 PROPERTIES OF PARALLELOGRAMS EXAMPLE Properties of Parallelograms Learn the notation given on page 330! Learn the definition of parallelograms and the theorems listed on page 330!

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Extra Example 1 EXAMPLE 2 GHJK is a parallelogram. Find the unknown length. a. JH b. LH GH J K L 6 8 Solution

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Extra Example 2 EXAMPLE 3 Solution

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Extra Example 3 XY ZW (3x + 18)° (4x - 9)° WXYZ is a parallelogram. Find the value of x. Solution

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Checkpoint UVWX is a parallelogram. XW VU Z 14 60° x = 19

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GOAL 2 REASONING ABOUT PARALLELOGRAMS EXAMPLE 4EXAMPLE Properties of Parallelograms

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Extra Example 4 AB C D

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Extra Example 5 A BC DEF

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Checkpoint EXAMPLE 6 A BC D F E You can use linear pairs to show that What postulate or theorem can you then use with the substitution and subtraction properties of equality and the definition of congruence to show that

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Extra Example 6 A four-sided concrete slab has consecutive angle measures of 85°, 94°, 85°, and 96°. Is the slab a parallelogram? Explain. No; if it were, then by Theorem 6.3 both pairs of opp. angles would be congruent, not just one pair.

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Checkpoint Each circle in the crystal lattice shown represents a molecule. ABED and BCFE are parallelograms. A, B, and C are collinear, as are D, E, and F. Must ACFD be a parallelogram? Explain. ABC FED Yes. Since segments AB and DE are parallel and contained in segments AC and DF, then segments AC and DF must be parallel. Also, since segments AD and CF are both parallel to segment BE, they are parallel to each other.

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QUESTION: ANSWER: What are 5 properties of parallelograms? 1. Opposite sides are parallel. 2. Opposite sides are congruent. 3. Opposite angles are congruent. 4. Consecutive angles are supplementary. 5. Diagonals bisect each other. BONUS POINT: 6. The sum of the interior angles is 360°.

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