1. Lesson 4 Menu 1.Determine whether the quadrilateral shown in the figure is a parallelogram. Justify your answer. 2.Determine whether the quadrilateral shown in the figure is a parallelogram. Justify your answer. 3.Use the Distance Formula to determine whether a figure with vertices A(3, 7), B(9, 10), C(10, 6), D(4, 3) is a parallelogram. 4.Use the Slope Formula to determine whether a figure with vertices R(2, 3), S(–1, 2), T(–1, –2), U(2, –2) is a parallelogram.

2. Lesson 4 MI/Vocab rectangle Recognize and apply properties of rectangles. Determine whether parallelograms are rectangles.

3. Lesson 4 TH1

4. Lesson 4 KC1

5. Lesson 4 Ex1 Quadrilateral RSTU is a rectangle. If RT = 6x + 4 and SU = 7x – 4, find x. Diagonals of a Rectangle

6. Lesson 4 Ex1 Answer: 8 Diagonals of a Rectangle The diagonals of a rectangle are congruent, Definition of congruent segments Substitution Subtract 6x from each side. Add 4 to each side. Diagonals of a rectangle are .

7. A.A B.B C.C D.D Lesson 4 CYP1 A.x = –1 B.x = 3 C.x = 5 D.x = 10 Quadrilateral EFGH is a rectangle. If FH = 5x + 4 and GE = 7x – 6, find x.

8. Lesson 4 Ex2 Angles of a Rectangle Quadrilateral LMNP is a rectangle. Find x.

9. Lesson 4 Ex2 Angles of a Rectangle Answer: 10 Angle Addition Postulate Substitution Simplify. Subtract 10 from each side. Divide each side by 8.

10. Lesson 4 CYP2 1.A 2.B 3.C 4.D A.6 B.7 C.9 D.14 Quadrilateral EFGH is a rectangle. Find x.

11. Lesson 4 TH2

12. Lesson 4 Ex3 Kyle is building a barn for his horse. He measures the diagonals of the door opening to make sure that they bisect each other and they are congruent. How does he know that the measure of each corner is 90? Diagonals of a Parallelogram We know that A parallelogram with congruent diagonals is a rectangle. Therefore, the corners are 90° angles. Answer:

13. Lesson 4 Ex4 Quadrilateral ABCD has vertices A(–2, 1), B(4, 3), C(5, 0), and D(–1, –2). Determine whether ABCD is a rectangle using the Slope Formula. Rectangle on a Coordinate Plane Method 1: Use the Slope Formula, to see if opposite sides are parallel and consecutive sides are perpendicular.

14. Lesson 4 Ex4 Answer:The perpendicular segments create four right angles. Therefore, by definition ABCD is a rectangle. Rectangle on a Coordinate Plane quadrilateral ABCD is a parallelogram. The product of the slopes of consecutive sides is –1. This means that

15. Lesson 4 Ex4 Rectangle on a Coordinate Plane Method 2: Use the Distance Formula, to determine whether opposite sides are congruent.

16. Lesson 4 Ex4 Rectangle on a Coordinate Plane Since each pair of opposite sides of the quadrilateral have the same measure, they are congruent. Quadrilateral ABCD is a parallelogram.

17. Lesson 4 Ex4 Find the length of the diagonals. Answer:Since the diagonals are congruent, ABCD is a rectangle. Rectangle on a Coordinate Plane The length of each diagonal is

18. 1.A 2.B 3.C Lesson 4 CYP4 A.yes B.no C.cannot be determined Quadrilateral WXYZ has vertices W(–2, 1), X(–1, 3), Y(3, 1), and Z(2, –1). Determine whether WXYZ is a rectangle using the Distance Formula.

19. A.A B.B C.C D.D Lesson 4 CYP4 What are the lengths of diagonals WY and XZ? A. B.4 C.5 D.25