Use Properties of Rectangles
If AB = 10 in rectangle ABCD, what is CD?
CD = 10
In rectangle ABCD, m∠DAC = 38. What is m∠CAB?
m∠CAB = 52.
In parallelogram ABCD, AB = 15. What is the value of CD so that ABCD is a rectangle?
CD = 15.
In rectangle ABCD, line AB = 32. What is line CD?
CD = 32
What is a rectangle?
In rectangle ABCD, m∠CAB = 37. What is m∠ACD?
m∠ACD = 37.
In rectangle ABCD, the two diagonals seg AC and seg BD meet at point E. If AE = 40, what is the value of BE + CE + DE?
BE + CE + DE = 120.
In parallelogram ABCD, AB = 6 and AD = 8. What is the value of BD to prove that ABCD is a rectangle?
In rectangle ABCD, the two diagonals seg AC and seg BD meet at point E. Name all segments congruent to seg AE.
seg BE, seg CE, and seg DE
In rectangle ABCD, m∠DAB = x2 + 14x - 5. What is the value of x?
x = 5.
In parallelogram ABCD, which pairs of lines should be congruent so that ABCD is a rectangle?
line AB and line DC ; line AD and line BC ; line AC and line BD
What are the two formulas you can use to prove if a quadrilateral is a rectangle?
Distance Formula and Slope Formula
In rectangle ABCD, the two diagonals seg AC and seg BD meet at point E. If m∠AEB = 111, what is m∠ADB?
m∠ADB = 55.5.
In rectangle ABCD, the two diagonals seg AC and seg BD meet at point E, and m∠DCA = 29. What is m∠AED?
m∠AED = 58.
State the theorem for proving that parallelograms are rectangles.
If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle.
Quadrilateral ABCD has vertices A(-10, 2), B(-8, -6), C(5, -3), and D(2, 5). Is quadrilateral ABCD a rectangle?
No.
State all five properties of rectangles.
All four angles are right angles.
Opposite sides are parallel and congruent.
Opposite angles are congruent.
Consecutive angles are supplementary.
Diagonals bisect each other.
In rectangle ABCD, the two diagonals seg AC and seg BD meet at point E, and m∠CAB = 5x - 5. If m∠DEC = 120, what is x + m∠ADB?
x + m∠ADB = 7 + 60 = 67.
State a paragraph proof of the following statement: If a parallelogram has one right angle, then it is a rectangle.
Assume ABCD is a parallelogram, and ∠B is a right angle. Because ABCD is a parallelogram and has one right angle, then it has four right angles (since opposite angles are congruent and consecutive angles are supplementary). So by the definition of a rectangle, ABCD is a rectangle.
Quadrilateral ABCD has vertices A(x, y), B(5, 5), C(6, -2) and D(-1, -3). What is the value of x + y?
x + y = -2 + 4 = 2.