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EXAMPLE 1

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EXAMPLE 1

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  1. Ride An amusement park ride has a moving platform attached to four swinging arms. The platform swings back and forth, higher and higher, until it goes over the top and around in a circular motion. In the diagram below, ADand BCrepresent two of the swinging arms, and DCis parallel to the ground (line l). Explain why the moving platform ABis always parallel to the ground. EXAMPLE 1 Solve a real-world problem

  2. By the definition of a parallelogram, AB DC. Because DCis parallel to line l, ABis also parallel to line l by the Transitive Property of Parallel Lines. So, the moving platform is parallel to the ground. EXAMPLE 1 Solve a real-world problem SOLUTION The shape of quadrilateral ABCDchanges as the moving platform swings around, but its side lengths do not change. Both pairs of opposite sides are congruent, so ABCDis a parallelogram by Theorem 8.7.

  3. 1. In quadrilateral WXYZ, m W = 42°,m X =138°, m Y = 42°. Find m Z. Is WXYZa parallelogram? Explain your reasoning. 360° m W + m K + m Y + m Z = 42° + 138° + 42° + m Z = 360° 360° m Z + 222° = m Z = 138° for Example 1 GUIDED PRACTICE SOLUTION Corollary to Theorem 8.1 Substitute Combine like terms. Subtract. Yes, since the opposite angles of the quadrilateral are congruent, WXYZ is a parallelogram.

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