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.
What do we know about a square's sides and angles?
A square has 4 congruent sides and 4 congruent (90 degree) angles.
Where did Mr. Brooks go to college?
Wright State University
If ABCD is a parallelogram and angle A = 2x + 40, and angle B = 3x - 10. Explain how you would set up the equation.
Add the expressions and set them equal to 180 degrees. ( Consecutive Angles are Supplementary )
ABCD is a rhombus, and the diagonals intersect at point E. What is the measure of <AEB?
90 degrees (diagonals are perpendicular)
In rectangle ABCD, AC = 7x and BD = 3x + 20. What is the value of x?
x = 5
Is a rhombus always a square? Explain.
No
What month is Mr. Brooks' birthday in?
March
If ABCD is a parallelogram, and AB = 3x - 5, and
BC = 6x - 2, and AD = 2x + 12. Explain the equation used to solve the problem.
Set the expressions for sides BC and AD equal to one another.
In rhombus ABCD, diagonals AC and BD intersect at E. If the measure of angle BAD = 72, what is the measure of angle CAD?
Angle CAD = 36, because the diagonals bisect the corner angles.
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
Name at least 4 properties of a square.
(DIAGONALS): perpendicular, congruent, bisect each other, bisect the angles (SIDES): all 4 sides are congruent, opposite sides parallel ( ANGLES): All 4 angles are congruent, consecutive angles are supplementary.
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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.
Name the 3 properties that the diagonals of a rhombus have.
diagonals bisect each other diagonals are perpendicular diagonals bisect the angles
MATH is a rectangle whose diagonals intersect at J. The measure of <MAH= 37 degrees, so find the measure of <AMT
m<AMT= 37 degrees
EFGH is a square whose diagonals intersect at point P. Find the measure of <FPG and <FEP.
<FPG=90 because diagonals are perpendicular, <FEP=45 because corner angles are bisected by diagonals
What is the street address (number and name) for Belleview High
10400 SE 36th Ave
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, because the diagonals bisect each other.
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.
a) Every rectangle is a square. b) Every square is a rectangle. Choose the correct statement and explain.
b) A square is a special type of rectangle. Some rectangles are squares, but not all as they do not necessarily have 4 congruent sides.
Square DEFG has DE=3x+2, EF=6+x, and EG=8. Solve for x.
x=2. Set DE=EF. EG is the diagonal.
What is the capital of Vermont?
Montepelier