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What constraints are needed on the lengths of the sides of a quadrilateral for it to be a parallelogram?
Both pairs of opposite sides need to be congruent (the same length).
If two angles are congruent then they are both right angles?
Not always. If two angles are congruent then they simply have equal measure. They must only be right angles if they are supplementary, that is, they must both add up to 180 degrees.
What are all of the characteristics of a parallelogram?
Parallelograms: 1.)opposite side of a parallelogram are parallel and you can prove that by finding the slope for both lines. 2.) opposite sides of a parallelogram are congruent 3.) diagonals bisect each other 4.)opposite angles are congruent 5.) consecutive angles are supp. *Remember that alternate interior angles are congruent. To break it down in a better understanding way. 1.)opposite side of a parallelogram are parallel and you can prove that by finding the slope for both lines. If the shape is a parallelogram then you can find the slope of its sides. if they are parallel to each other then it is a parallelogram. 2.) opposite sides of a parallelogram are congruent top and bottom sides are congruent. right and left sides are congruent. 3.) diagonals bisect each other When you draw a straight line from the top right corner to the bottom left corner and from the top left corner to the bottom right corner, the bisect each other or in better terms, the lines cut each other equaly in half. 4.)opposite angles are congruent just as the sides. 5.) consecutive angles are supp. These angels produce a line. this line like all lines will add up to 180 degrees. *Remember that alternate interior angles are congruent.
What is the four right angles theorem?
The theorem states "If two angles are both supplementary and congruent, then they are right angles."
Among two congruent angles one has a measure of 100 the measure of the other angle is?
Exactly the same because they are both congruent
Are both pairs of opposite angles are congruent in a parrallelogram?
Yes, both pairs of opposite angles in a parallelogram are congruent.
If both pairs of opposite angles of a quadrilateral are congruent then the quadrilateral is not a parallelogram?
False. If both pairs of opposite angles of a quadrilateral are congruent then the quadrilateral is a parallelogram.
What is always true about parallelograms?
Both pairs of opposite sides are parallel + congruent, and both pairs of opposite angles are also congruent.
Can congruent angles determine if there is a parallelogram?
If both pairs of opposite angles of a quadrilateral are congruent, then it is a parallelogram.
What are five characteristics of a rectangle?
* both pairs of opposite sides are parallel * both pairs of opposite sides are congruent * all angles are 90 degrees * both pairs of opposite angles are congruent * the diagonals bisect each other.
What shape have both pairs of opposite angles that are congruent?
How about a square or a rectangle
Are both pairs of opposite angles of a parallelogram are always congruent?
Yes
If one pair of opposite angles of a quadrilateral are congruent and one pair of opposite angles are congruent then is the quadrilateral a parallelogram?
For the quadrilateral to be a parallelogram, both pairs of opposite angles must be congruent.
What is one way to prove that a quadrilateral is a parallegram?
* both pairs of opposite sides are parallel * both pairs of opposite sides are congruent * both pairs of opposite angles are congruent * one pair of opposite sides are parallel and congruent * both diagonals bisect each other * all consecutive angle pairs are supplementary
If both pairs of opposite angles of a quadrilateral are congruent is the quadrilateral a parallelogram?
Yes
If both pairs of opposite angles of a quadrilateral are congruent then the quadrilateral is a parallelogram?
True
What do you call a quadrilateral having both pairs of opposite angles congruent?
A parallelogram.
