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EXAMPLE 2

ARCHITECTURE. In the photograph, ST UV and ST UV . By Theorem 8.9, quadrilateral STUV is a parallelogram. EXAMPLE 2. Identify a parallelogram.

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EXAMPLE 2

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  1. ARCHITECTURE In the photograph, ST UVand ST UV. By Theorem 8.9, quadrilateral STUVis a parallelogram. EXAMPLE 2 Identify a parallelogram The doorway shown is part of a building in England. Over time, the building has leaned sideways. Explain how you know that SV =TU. SOLUTION By Theorem 8.3, you know that opposite sides of a parallelogram are congruent. So, SV = TU.

  2. For what value of xis quadrilateral CDEFa parallelogram? ALGEBRA By Theorem 8.10, if the diagonals of CDEFbisect each other, then it is a parallelogram. You are given that CNEN. Find xso that FN DN. EXAMPLE 3 Use algebra with parallelograms SOLUTION

  3. ANSWER Quadrilateral CDEF is a parallelogram when x = 4. EXAMPLE 3 Use algebra with parallelograms DN FN = Set the segment lengths equal. 3x 5x – 8 = Substitute 5x –8 for FN and 3xfor DN. 0 2x – 8 = Subtract 3xfrom each side. 8 2x = Add 8 to each side. 4 x = Divide each side by 2. FN = 5(4) –8 = 12 andDN = 3(4) = 12. Whenx = 4,

  4. 2. ANSWER In the graphic, two opposite sides are equal, i.e, 30m each and parallel, Therefore, the quadrilateral is a parallelogram. By theorem 8.9. for Examples 2 and 3 GUIDED PRACTICE What theorem can you use to show that the quadrilateral is a parallelogram?

  5. 3. ANSWER Two pairs of opposite sides are equal. Therefore, the quadrilateral is a parallelogram. By theorem 8.7 for Examples 2 and 3 GUIDED PRACTICE What theorem can you use to show that the quadrilateral is a parallelogram?

  6. 4. ANSWER By theorem 8.8, if the opposite angles are Congruent, the quadrilateral is a parallelogram. for Examples 2 and 3 GUIDED PRACTICE What theorem can you use to show that the quadrilateral is a parallelogram?

  7. 5. For what value of xis quadrilateral MNPQa parallelogram? Explain your reasoning. 2x = 10 – 3x By Theorem 8.6 [ Diagonals in bisect each other ] 5x = 10 x = 2 for Examples 2 and 3 GUIDED PRACTICE SOLUTION Add 3xto each side Divide each side by 5

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