Parallelograms
Name a property that the diagonals of a parallelogram have.
The diagonals bisect each other.
Name the 2 properties that the diagonals of a rectangle have.
They are congruent and bisect each other.
In Rhombus MNOP, MN = 24, and NO = 2x + 6. What is the value of x?
x = 9
How do you prove a rectangle is a square?
Show it has 2 congruent adjacent sides. Also acceptable, show all 4 sides are congruent.
If a parallelogram has a 90 degree angle at the corner then it is a rectangle.
True or False.
True
If ABCD is a parallelogram and angle A = 2x + 40, and angle B = 3x - 10. Find the value of Angle A.
100
In rectangle ABCD, AC = 7x and BD = 3x + 20. What is the value of x?
x = 5.
In Rhombus MNOP the diagonals intersect at point Q. If Angle MNO = 112 degrees what is the measure of angle MNQ?
56
In Square ABCD AB = 2x - 13 and BC = x + 17 find the length of AB.
AB = 47.
A quadrilateral has the following properties: Its diagonals bisect the angles. Its diagonals are not congruent. Choose any of the following that it could be. I.) rhombus II.) rectangle III.) parallelogram IV.) square
I.) rhombus only
If ABCD is a parallelogram, and AB = 3x - 5, and BC = 6x - 2, and AD = 2x + 12. Find AB.
AB = 5.5
In rectangle ABCD, the diagonals intersect at E. AE = 4x + 20, BC = 7x + 12 and DE = 8x + 4. What is the value of x?
x = 4
In rhombus ABCD, diagonals AC and BD intersect at E. If the measure of angle BAD = 72, what is the measure of angle CED?
Angle CED = 90
If the diagonals of square ABCD intersect at point E. What is the measure of Angle ABE?
Angle ABE = 45 degrees.
What else do you need to show to say a Parallelogram is a Rectangle?
The 4 major angles are 90 degrees.
To prove a quadrilateral is a parallelogram, show which of the following: ( You may choose more than one. ) I.) Both pairs of opposite sides are congruent. II.) Both pairs of opposite sides are parallel. III.) One pair of sides are parallel and congruent. IV.) The diagonals are congruent.
I, II, and III only. The diagonals are not congruent, they BISECT EACH OTHER.
In Rectangle ABCD who are the consecutive angles?
A - B
B - C
C - D
A - D
Name the 3 properties that the diagonals of a rhombus have.
diagonals bisect each other
diagonals are perpendicular
diagonals bisect the angles
If the Diagonals of the square ABCD intersect at point E. What is the measure of Angle AEB?
Angle AEB = 90 b/c property of a square the diagonals are perpendicular.
All my sides are congruent and my diagonals are congruent what am I?
Square
In parallelogram ABCD, diagonals AC and BD intersect at E. If angle A = 85, and AE = 3x + 10, and EC = 7x - 30, Find the measure of angle C and the value of x.
Angle C is 85 degrees, and x = 10, b/c the diagonals bisect each other.
The Diagonals in Rectangle ABCD intersect at point E. AC = 4x - 15 and BD = 3x + 23 find the value of AE.
AE = 68.5
In rhombus ABCD, the diagonals are drawn and intersect at E. If AC = 20, and BD = 48, what is the measure of AB?
Use the fact that the diagonals bisect each other and are perpendicular. Each right triangle has legs of 10 and 24. Use the pythagorean theorem to figure out that AB = 26.
One side of a square is 5 cm. What is the length of the diagonal of the square?
sqrt(50)
I have 4 parallel sides and my diagonals bisect each other, but are not congruent. Opposite sides are congruent to each other, but not all 4 sides. What am I?
Parallelogram.