lesson 4 menu 1.determine whether the quadrilateral shown in the figure is a parallelogram. justify...
TRANSCRIPT
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.
• rectangle
• Recognize and apply properties of rectangles.
• Determine whether parallelograms are rectangles.
Quadrilateral RSTU is a rectangle. If RT = 6x + 4 and SU = 7x – 4, find x.
Diagonals of a Rectangle
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 .
A. A
B. B
C. C
D. D
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.
Angles of a Rectangle
Answer: 10
Angle Addition Postulate
Substitution
Simplify.
Subtract 10 from each side.Divide each side by 8.
1. A
2. B
3. C
4. D
A. 6
B. 7
C. 9
D. 14
Quadrilateral EFGH is a rectangle. Find x.
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:
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.
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
Rectangle on a Coordinate Plane
Method 2: Use the Distance Formula,
to determine whether opposite sides are congruent.
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.
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
1. A
2. B
3. C
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.
A. A
B. B
C. C
D. D
What are the lengths of diagonals WY and XZ?
A.
B. 4
C. 5
D. 25