1/8/2016 Five-Minute Check (over Lesson 6 3) CCSS Then/Now New Vocabulary Theorem 6.13: Diagonals of a Rectangle Example 1: Real-World Example: Use Pr

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1 Five-Minute Check (over Lesson 6 3) CCSS Then/Now New Vocabulary Theorem 6.13: Diagonals of a Rectangle Example 1: Real-World Example: Use Properties of Rectangles Example 2: Use Properties of Rectangles and Algebra Theorem 6.14 Example 3: Real-World Example: Proving Rectangle Relationships Example 4: Rectangles and Coordinate Geometry 1

2 (1-2) Determine whether the quadrilateral is a parallelogram and state your reasoning. Use the Distance Formula to determine if A(3, 7), B(9, 10), C(10, 6), D(4, 3) are the vertices of a parallelogram. Use the Slope Formula to determine if R(2, 3), S( 1, 2), T( 1, 2), U(2, 2) are the vertices of a parallelogram. Determine whether the quadrilateral is a parallelogram. A. Yes, all sides are congruent. B. Yes, all angles are congruent. C. Yes, diagonals bisect each other. D. No, diagonals are not congruent. 2

3 Determine whether the quadrilateral is a parallelogram. A. Yes, both pairs of opposite angles are congruent. B. Yes, diagonals are congruent. C. No, all angles are not congruent. D. No, side lengths are not given. Use the Distance Formula to determine if A(3, 7), B(9, 10), C(10, 6), D(4, 3) are the vertices of a parallelogram. A. yes B. no 3

4 Use the Slope Formula to determine if R(2, 3), S( 1, 2), T( 1, 2), U(2, 2) are the vertices of a parallelogram. A. yes B. no Given that QRST is a parallelogram, which statement is true? A. m S = 105 B. m T = 105 C. QT ST D. QT QS 4

5 Content Standards G.CO.11 Prove theorems about parallelograms. G.GPE.4 Use coordinates to prove simple geometric theorems algebraically. Mathematical Practices 3 Construct viable arguments and critique the reasoning of others. 5 Use appropriate tools strategically. You used properties of parallelograms and determined whether quadrilaterals were parallelograms. Recognize and apply properties of rectangles. Determine whether parallelograms are rectangles. 5

6 Rectangle Parallelogram with 4 right angles Properties Opposite sides are parallel and congruent Opposite angles are congruent Consecutive angles are supplementary Diagonals bisect each other Diagonals are congruent Quadrilateral EFGH is a rectangle. If GH = 6 feet and FH = 15 feet, find GJ. A. 3 feet B. 7.5 feet C. 9 feet D. 12 feet 6

7 Use Properties of Rectangles and Algebra Quadrilateral RSTU is a rectangle. If m RTU = 8x + 4 and m SUR = 3x 2, find x. m SUT + m SUR = 90 m RTU + m SUR = 90 8x x 2 = 90 11x + 2 = 90 11x = 88 x = 8 Quadrilateral EFGH is a rectangle. If m FGE = 6x 5 and m HFE = 4x 5, find x. A. x = 1 B. x = 3 C. x = 5 D. x = 10 7

8 Proving Rectangle Relationships ART Some artists stretch their own canvas over wooden frames. This allows them to customize the size of a canvas. In order to ensure that the frame is rectangular before stretching the canvas, an artist measures the sides and the diagonals of the frame. If AB = 12 inches, BC = 35 inches, CD = 12 inches, DA = 35 inches, BD = 37 inches, and AC = 37 inches, explain how an artist can be sure the frame is rectangular. 8

9 Max is building a swimming pool in his backyard. He measures the length and width of the pool so that opposite sides are parallel. He also measures the diagonals of the pool to make sure that they are congruent. How does he know that the measure of each corner is 90? A. Since opp. sides are, STUR must be a rectangle. B. Since opp. sides are, STUR must be a rectangle. C. Since diagonals of the are, STUR must be a rectangle. D. STUR is not a rectangle. Rectangles and Coordinate Geometry Quadrilateral JKLM has vertices J( 2, 3), K(1, 4), L(3, 2), and M(0, 3). Determine whether JKLM is a rectangle using the Distance Formula. Step 1 Use Distance Formula to confirm JKLM is a parallelogram (i.e. eliminate possibility of trapezoid). = + = = 10 = = 10 = = 40 = = 40 Since opposite sides are congruent JKLM is a parallelogram. 9

10 Rectangles and Coordinate Geometry Quadrilateral JKLM has vertices J( 2, 3), K(1, 4), L(3, 2), and M(0, 3). Determine whether JKLM is a rectangle using the Distance Formula. Step 2 Use Distance Formula to determine whether JKLM is a rectangle. = + = = 50 = = 50 Since diagonals are congruent JKLM is a rectangle. Quadrilateral WXYZ has vertices W( 2, 1), X( 1, 3), Y(3, 1), and Z(2, 1). Determine whether WXYZ is a rectangle by using the Distance Formula. A. yes B. no C. cannot be determined 10

11 Quadrilateral WXYZ has vertices W( 2, 1), X( 1, 3), Y(3, 1), and Z(2, 1). What are the lengths of diagonals WY and XZ? A. B. 4 C. 5 D