Example 1 Identify Parallelograms Determine whether the quadrilateral is a parallelogram. Justify your answer. Answer:If both pairs of opposite sides of a quadrilateral are congruent, the quadrilateral is a parallelogram.
Example 1 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?
Example 2 Use Parallelograms to Prove Relationships MECHANICS Scissor lifts, like the platform lift shown, are commonly applied to tools intended to lift heavy items. In the diagram, A C and B D. Explain why the consecutive angles will always be supplementary, regardless of the height of the platform.
Example 2 Use Parallelograms to Prove Relationships Answer:Since both pairs of opposite angles of quadrilateral ABCD are congruent, ABCD is a parallelogram by Theorem 6.10. Theorem 6.5 states that consecutive angles of parallelograms are supplementary. Therefore, m A + m B = 180 and m C + m D = 180. By substitution, m A + m D = 180 and m C + m B = 180.
Example 2 The diagram shows a car jack used to raise a car from the ground. In the diagram, AD BC and AB DC. Based on this information, which statement will be true, regardless of the height of the car jack. A. A B B. A C C.AB BC D.m A + m C = 180
Example 3 Use Parallelograms and Algebra to Find Values Find x and y so that the quadrilateral is a parallelogram.
Example 3 A.m = 2 B.m = 3 C.m = 6 D.m = 8 Find m so that the quadrilateral is a parallelogram.