Chapter 6 – Quadrilaterals Lesson 6.4 – Rectangles Rectangle: A ...

Chapter 6 – QuadrilateralsLesson 6.4 – RectanglesRectangle: A quadrilateral with 4 right angles.Because a rectangle is a parallelogram, it has all the properties of theparallelogram in addition to the properties exclusive to the rectangle.Lesson 6.4 – Page 1

Example 1: Quadrilateral RSTU is a rectangle. IfRT = 6x + 4 and SU = 7x – 4, find x.7x – 4 = 6x + 4x – 4 = 4x = 8NOW TRY THIS: Quadrilateral ABCD is a rectangle.If AC = 5x + 4 and BD = 7x – 6, find x.7x – 6 = 5x + 42x – 6 = 42x = 10x = 5Example 2: Quadrilateral LMNP is a rectangle. Find x and y.3x + 2 + 5x + 8 = 908x + 10 = 908x = 80x = 106y + 2 = 906y = 88y = 14NOW TRY THIS: QuadrilateralABCD is a rectangle. Find x and y.9x + 20 + 4x + 5 = 9013x + 25 = 9013x = 65x = 54y + 4 = y 2 -1y 2 – 4y – 4 – 1 = 0y 2 – 4y -5 = 0 Use the graphing calc to find y = 5.Lesson 6.4 – Page 2

Example 3: Kyle is building a barn for his horse. He measures the diagonals ofthe door opening to make sure they bisect each other and they are congruent.How does he know that the measure of each corner is 90°?If the diagonals are congruent, then it is a rectangle. Arectangle has 4 right angles.Example 4: Quadrilateral ABCD has vertices A(-2, 1), B(4, 3), C(5, 0), andD(-1, -2). Determine whether ABCD is a rectangle.Finding the slope of each line shows thatthe lines are perpendicular. (-3, -3, 1/3, 1/3)If the lines are perpendicular, then youhave right angles. Therefore it is arectangle.Lesson 6.4 – Page 3

NOW TRY THIS: Quadrilateral FGHJ has vertices F(-4, -1), G(-2, -5), H(4, -2), andJ(2, 2). Determine whether FGHJ is a rectangle.Since the slopes are -2, -2, ½ & ½, the lines areperpendicular. Therefore, there are 4 rightangles, and the shape is a rectangle.Lesson 6.4 – Page 4