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Five-Minute Check (over Lesson 6–3)
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
Over Lesson 6–3
A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
A. Yes, all sides are congruent.
B. Yes, all angles are congruent.
C. Yes, diagonals bisect each other.
D. No, diagonals are not congruent.
Determine whether the quadrilateral is a parallelogram.
Over Lesson 6–3
A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
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.
Determine whether the quadrilateral is a parallelogram.
Over Lesson 6–3
A. yes
B. no
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. A
B. B
A B
0%0%
Over Lesson 6–3
A. yes
B. no
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. A
B. B
A B
0%0%
Over Lesson 6–3
A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
Given that QRST is a parallelogram, which statement is true?
A. mS = 105
B. mT = 105
C. QT ST
D. QT QS
______
___ ___
You used properties of parallelograms and determined whether quadrilaterals were parallelograms. (Lesson 6–2)
• Recognize and apply properties of rectangles.
• Determine whether parallelograms are rectangles.
Use Properties of Rectangles
CONSTRUCTION A rectangular garden gate is reinforced with diagonal braces to prevent it from sagging. If JK = 12 feet, and LN = 6.5 feet, find KM.
Use Properties of Rectangles
Since JKLM is a rectangle, it is a parallelogram. The diagonals of a parallelogram bisect each other, so LN = JN.
JN + LN = JL Segment Addition
LN + LN = JL Substitution
2LN = JL Simplify.
2(6.5) = JL Substitution
13 = JL Simplify.
Use Properties of Rectangles
Answer: KM = 13 feet
JL = KM Definition of congruence
13 = KM Substitution
JL KM If a is a rectangle,diagonals are .
A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
A. 3 feet
B. 7.5 feet
C. 9 feet
D. 12 feet
Quadrilateral EFGH is a rectangle. If GH = 6 feet and FH = 15 feet, find GJ.
Use Properties of Rectangles and Algebra
Quadrilateral RSTU is a rectangle. If mRTU = 8x + 4 and mSUR = 3x – 2, find x.
Use Properties of Rectangles and Algebra
mSUT + mSUR = 90 Angle Addition
mRTU + mSUR = 90 Substitution
8x + 4 + 3x – 2 = 90 Substitution
11x + 2 = 90 Add like terms.
Since RSTU is a rectangle, it has four right angles. So, mTUR = 90. The diagonals of a rectangle bisect each other and are congruent, so PT PU. Since triangle PTU is isosceles, the base angles are congruent so RTU SUT and mRTU = mSUT.
Use Properties of Rectangles and Algebra
Answer: x = 8
11x = 88 Subtract 2 from eachside.
x = 8 Divide each side by 11.
A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
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 the Distance Formula to determinewhether JKLM is a parallelogram bydetermining if opposite sides are congruent.
Rectangles and Coordinate Geometry
Since opposite sides of a quadrilateral have the same measure, they are congruent. So, quadrilateral JKLM is a parallelogram.
Rectangles and Coordinate Geometry
Answer: Since the diagonals have the same measure, they are congruent. So JKLM is a rectangle.
Step 2 Determine whether the diagonals of JKLMare congruent.
1. A
2. B
3. C
0% 0%0%
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 by using the Distance Formula.
A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
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. 25
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