Properties of Parallelograms
The relationship between the opposite sides of a parallelogram.
What is opposite sides of a parallelogram are congruent?
The sum of the exterior angles of a nonogon?
What is 360 degrees?
(The sum of the exterior angles is always 360 degrees regardless of the number of sides the polygon has).
ABCD is a parallelogram, AB = 3x - 5, BC = 6x - 2, and AD = 2x + 12. Write the equation used to solve for x.
What is 6x - 2 = 2x + 12 ?
(Opposite sides are congruent)
The sum of the measure of the interior angles of a triangle.
What is 180 degrees?
The relationship between opposite angles of a parallelogram.
What is the opposite angles of a parallelogram are congruent?
The sum of the measures of the interior angles of a convex hexagon.
What is 720 degrees?
Sum interior angles = (n-2)180
ABCD is a parallelogram. Angle A = 2x + 40, angle B = 3x - 10. Write an equation to solve for x.
What is 2x + 40 + 3x - 10 = 180 ?
( Consecutive Angles are Supplementary )
The equation to solve for x given angle ABC with ray BD in the interior of angle ABC. Measure of angle ABC is 50 degrees. Measure of angle ABD is 20 degrees. Measure of angle DBC is 2x - 10.
What is 2x - 10 + 20 = 50?
(Angle Addition Postulate; the sum of the two interior angles equals the measure of the angle).
The relationship between consecutive angles of a parallelogram.
What is consecutive angles of a parallelogram are supplementary (=180 degrees)?
Sum of the measures of the interior angles of a 46-gon?
What is 7920 degrees?
(46-2)180
Equation to solve for x given pentagon ABCDE with angle A = 3x - 11, angle B = x + 8, angle C = x, angle D = 2x + 7, angle E = x - 8.
What is (5-2)180 = 3x-11 + x+8 + x + 2x+7 + x-8?
Or
What is 540 = 8x - 4 ?
(n-2)180 = m <A + m <B + m<C + m<D + m<E
The relationship between alternate interior angles of parallel lines?
What is congruent?
The property that the diagonals of a parallelogram have.
What is diagonals bisect each other?
The measure of each exterior angle of a regular octagon.
What is 45 degrees?
360/8
The slope of RS in parallelogram RSTW, given the slope of ST is 3/2 and the slope of TW is -1/3
What is m = -1/3?
(Slopes of parallel lines are equal).
The slope formula.
What is m = (y2-y1)/(x2-x1)
OR What is m = rise/run
The ways to prove a quadrilateral is a parallelogram: ( You may choose more than one. ) I.) Show both pairs of opposite sides are congruent. II.) Show both pairs of opposite sides are parallel. III.) Show one pair of sides are parallel and congruent. IV.) Show the diagonals are congruent.
What is I, II, and III? (Diagonals are not necessarily congruent, they bisect each other).
The number of degrees in one interior angle of a regular pentagon?
What is 108 degrees?
(5-2)180 / 5
The value of x and the measure of angle C, given parallelogram ABCD with diagonals AC and BD that intersect at E, if angle A = 85, and AE = 3x + 10, and EC = 7x - 30.
What is x = 10 and measure of angle C = 85 degrees?
(The diagonals bisect each other so 1/2 of a diagonal is equal to the other half of the same diagonal or 3x + 10 = 7x - 30).
(Opposite angles are congruent).
The distance formula.
What is Distance = Square Root of ((y2-y1)2 + (x2-x1)2) ?