Exploring Rectangles: Properties and Theorems in Geometry
In this lesson, you will learn to recognize and apply the properties of rectangles, a specific type of quadrilateral characterized by having four right angles. We will discuss the theorems related to rectangles, including how to determine if a parallelogram is also a rectangle based on its diagonals. You will also engage in problem-solving involving the dimensions and coordinates of rectangles. This foundational understanding is crucial in various mathematical contexts, laying the groundwork for further studies in geometry.
Exploring Rectangles: Properties and Theorems in Geometry
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Presentation Transcript
8.4 Rectangles What you’ll learn: To recognize and apply properties of rectangles. To determine whether parallelograms are rectangles.
Rectangles Rectangle – a quadrilateral with 4 right angles. Theorem 8.13 If a parallelogram is a rectangle, then the diagonals are congruent. Rectangles have all the properties of parallelograms plus 2 these 2.
Properties of rectangles • Opposite sides parallel. • Opposite sides congruent. • Opposite angles are congruent. • Consecutive angles supplementary. • Diagonals bisect each other. • All four angles are right angles. • Diagonals are congruent.
Theorem 8.14 If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle.
Quadrilateral RSTU is a rectangle. If RT=6x+4 and SU=7x-4, find x. If RS=x²+9 and TU=2x+44, find x. x²+9=2x+44 x²-2x-35=0 (x-7)(x+5)=0 x-7=0 x+5=0 x=7, -5 S T R U
Determine whether ABCD is a rectangle. • A(-4,3), B(-2,4), C(1,-2), D(-1,-3) • A(0,5), B(4,7), C(5,4), D(1,2)
