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Properties and Examples of Rectangles

Learn about rectangles, a special type of parallelogram with specific properties including congruent diagonals and equal opposite sides and angles. Explore examples such as finding side lengths and angle measures.

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Properties and Examples of Rectangles

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  1. Rectangles Lesson 6-3 Lesson 6-3: Rectangles

  2. Rectangles Definition: A rectangle is a parallelogram with four right angles. • Opposite sides are parallel. • Opposite sides are congruent. • Opposite angles are congruent. • Consecutive angles are supplementary. • Diagonals bisect each other. A rectangle is a special type of parallelogram. Thus a rectangle has all the properties of a parallelogram. Lesson 6-3: Rectangles

  3. A B E D C Properties of Rectangles Theorem: If a parallelogram is a rectangle, then its diagonals are congruent. Therefore, ∆AEB, ∆BEC, ∆CED, and ∆AED are isosceles triangles. Converse: If the diagonals of a parallelogram are congruent , then the parallelogram is a rectangle. Lesson 6-3: Rectangles

  4. A B 2 3 1 E 4 5 6 D C Examples……. • If AE = 3x +2 and BE = 29, find the value of x. • If AC = 21, then BE = _______. • If m<1 = 4x and m<4 = 2x, find the value of x. • If m<2 = 40, find m<1, m<3, m<4, m<5 and m<6. x = 7 units 10.5 units x = 18 units m<1=50, m<3=40, m<4=80, m<5=100, m<6=40 Lesson 6-3: Rectangles

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