Parallelograms
Name the two properties about the sides of a parallelogram.
What are opposite sides are congruent and opposite sides are parallel?
Name one of the 2 properties that differentiates a rectangle from a generic parallelogram.
What is the diagonals are congruent or there are four right angles (adjacent sides are perpendicular)?
Name the 3 properties that the diagonals of a rhombus have.
diagonals bisect each other
diagonals are perpendicular
diagonals bisect the angles
I am a parallelogram, a rectangle and a rhombus.
What is a square?
It is in these two 4-sided figures the diagonals are congruent.
What are a rectangle and a square?
This is the property of a parallelogram's diagonals.
What is the diagonals bisect each other?
In rectangle ABCD, AC = 7x and BD = 3x + 20. Find x.
What is x = 5?
7x = 3x + 20
Explain why a rhombus cannot be a square.
What is a rhombus doesn't have a right angle.
The sum of the lengths of the diagonals of a square is 12 cm. This is the length of one diagonal.
6 (diagonals are congruent so divide the sum by 2)
You would choose 1 or more of the following to prove a quadrilateral is a parallelogram
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.
This is true about the opposite angles in a parallelogram.
What is opposite angles are congruent?
If a parallelogram is a Rhombus, then its diagonals are...
What are perpendicular?
In rhombus ABCD, diagonals AC and BD intersect at E. If the measure of angle BAD = 72, find the measure of angle CDE.
What is 54 degrees?
(diagonals bisect the angles...If <BAD is 72, <CDA is 108 (consecutive angles). <CDE is half.
In Square ABCD , this is the measure of angle ABD
What is 45 degrees?
A: "Every rectangle is a square."
B: "Every square is a rectangle."
Choose the correct statement and explain.
A square is a special type of rectangle. Some rectangles are squares, but not all as they do not necessarily have 4 congruent sides.
This is the property shared by consecutive angles in a parallelogram.
What is that consecutive angles are supplementary?
The rectangles diagonals form 4 of these type of triangles (2 identical pairs)
What are isosceles triangles?
The diagonals in a rhombus from 4 of these type of traingles?
Name at least 4 properties of a square that aren't shared by other ordinary parallelograms.
(DIAGONALS): perpendicular, congruent, bisect the angles
(SIDES): all 4 sides are congruent
( ANGLES): All 4 angles are congruent
A parallelogram with four congruent sides and congruent diagonals.
What is a square?
Given parallelogram ABCD with diagonals intersecting at E, and AC = 50, this is the length of AE.
What is 25?
To prove a parallelogram is a rectangle one must show this to be true. (more than one option)
What is diagonals are congruent?
What is a pair of adjacent sides are perpendicular (forming a right angle)?
A special parallelogram that has perpendicular diagonals. (Need all answers to get credit).
What are a rhombus and a square?
The diagonals of a square form four of these types of triangles.
What are isosceles right triangles?
Two consecutive side lengths of a parallelogram are
3x + 8 and 2x - 5. The perimeter of the parallelogram
is 136. This is the value of x.
What is 13?
sum of sides is 10x +6 = 136