6-3 Tests for Parallelograms You recognized and applied properties of parallelograms. Recognize the conditions that ensure a quadrilateral is a parallelogram. Prove that a set of points forms a parallelogram in the coordinate plane.
Properties of Parallelograms The opposite sides of a parallelogram are parallel (by definition). The opposite angles of a parallelogram are congruent. The opposite sides of a parallelogram are congruent. The consecutive angles of a parallelogram are supplementary. The diagonals of a parallelogram bisect each other.
Write the Converse of the definition The opposite sides of a parallelogram are parallel (by definition). A quadrilateral is a parallelogram if both pairs of opposite sides are parallel (definition). 1.Draw a parallelogram on a piece of graph paper. 2.How do you check for 2 pairs of parallel sides?
Write the converse of: The opposite angles of a parallelogram are congruent. If both pairs of angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram. 1. Measure the angles of your parallelogram.
Write the Converse of The opposite sides of a parallelogram are congruent. If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. 1. Measure the length of the sides of your quadrilateral. Write down the measurements.
Write the Converse of The consecutive angles of a parallelogram are supplementary. If the consecutive angles of a quadrilateral are supplementary, then the quadrilateral is a parallelogram. 1. Add up the measures of the consecutive angles. Are they supplementary?
Write the Converse of The diagonals of a parallelogram bisect each other. If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. 1.Draw diagonals in your quadrilateral. 2.Measure the diagonals. 3.Measure each part of the diagonals and write down the measurement.
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Is the quadrilateral a parallelogram? Yes, Opposite sides are congruent. Yes, consecutive angles are supplementary. Yes, diagonals bisect each other. ?? The congruent sides may not be parallel. 70°110°
Determine whether the quadrilateral is a parallelogram. Justify your answer. Answer:Each pair of opposite sides has the same measure. Therefore, they are congruent. If both pairs of opposite sides of a quadrilateral are congruent, the quadrilateral is a parallelogram.
A.Both pairs of opp. sides ||. B.Both pairs of opp. sides . C.Both pairs of opp. s . D.One pair of opp. sides both || and . Which method would prove the quadrilateral is a parallelogram?
Find x and y so that the quadrilateral is a parallelogram. Opposite sides of a parallelogram are congruent. Substitution Distributive Property Add 1 to each side. Subtract 3x from each side. AB = DC
Answer:So, when x = 7 and y = 5, quadrilateral ABCD is a parallelogram. Substitution Distributive Property Add 2 to each side. Subtract 3y from each side.
COORDINATE GEOMETRY Quadrilateral QRST has vertices Q(–1, 3), R(3, 1), S(2, –3), and T(–2, –1). Determine whether the quadrilateral is a parallelogram. Justify your answer by using the Slope Formula. If the opposite sides of a quadrilateral are parallel, then it is a parallelogram. Answer:Since opposite sides have the same slope, QR║ST and RS║TQ. Therefore, QRST is a parallelogram by definition.
Conditions for a Parallelogram A quadrilateral is a parallelogram if both pairs of opposite sides are parallel (definition). If both pairs of angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram. If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. If the consecutive angles of a quadrilateral are supplementary, then the quadrilateral is a parallelogram. If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.
6-3 Assignment Page 418, 9-14, Show your work! No work, No credit