EXAMPLE 2 Identify a parallelogram ARCHITECTURE

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Presentation transcript:

EXAMPLE 2 Identify a parallelogram ARCHITECTURE 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 In the photograph, ST UV and ST UV. By Theorem 8.9, quadrilateral STUV is a parallelogram. By Theorem 8.3, you know that opposite sides of a parallelogram are congruent. So, SV = TU.

EXAMPLE 3 Use algebra with parallelograms ALGEBRA For what value of x is quadrilateral CDEF a parallelogram? SOLUTION By Theorem 8.10, if the diagonals of CDEF bisect each other, then it is a parallelogram. You are given that CN EN . Find x so that FN DN .

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

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

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

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

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