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GEOMETRY
LESSON 8-4
Pg 424-430
RECTANGLES
Objectives: 1. Recognize and apply the properties of rectangles
2. Determine whether parallelograms are rectangles and vice versa
Rectangle: A four-sided figure (quadrilateral) with both pairs of opposite sides parallel and congruent and with
all angles equal to 90 degrees.
Key Concepts: (Compare a rectangle to the parallelogram Key Concepts)
1)
2)
3)
4)
5)
6)
Opposite sides are parallel (same as parallelogram)
Opposite sides are congruent (same as parallelogram)
Opposite angles are congruent (same as parallelogram)
Consecutive angles are supplementary (total 180 degrees) (same as parallelogram)
Diagonals bisect each other (same with parallelogram)
Either diagonal will separate the rectangle into two congruent triangles (same with parallelogram)
Question 1: Are all rectangles also parallelograms??
Follow-Up Question 2: Then are all parallelograms then rectangles???
Rules for Rectangles (Unique to the Rectangle as compared to Parallelograms)
1. Opposite sides are parallel, but also perpendicular to adjacent sides (negative reciprocal slopes)
2. Both opposite and consecutive angles are congruent and always equal 90 degrees (right angles)
3. Diagonals not only bisect each other, but are congruent to each other.
THEREFORE: A rectangle is simply a parallelogram with CONGRUENT DIAGNALS
Let’s now do Problems 5, 6, 14, and 28 together