91Ó°ÊÓ

Draw and label a diagram. List what is given and what is to be proved. Then write a two-column proof of the theorem.

Theorem 5-5.

Parallel rulers, used to draw parallel lines, are constructed so that $\mathrm{EF}=\mathrm{HG}$and $\mathrm{HE}=\mathrm{GF}$. Since there are hinges at points E, F, G and H, you can vary the distance between role="math" localid="1637730770232" $\stackrel{↔}{HG}$and role="math" localid="1637730792914" $\stackrel{↔}{\mathrm{EF}}$. Explain why $\stackrel{↔}{\mathrm{HG}}$and $\stackrel{↔}{\mathrm{EF}}$are always parallel.

The perimeter of is $â–\pm \mathrm{STOP}$is role="math" localid="1637646034342" $54\mathrm{cm}$and role="math" localid="1637645233165" $\stackrel{¯}{ST}$is role="math" localid="1637646039176" $1\mathrm{cm}$ longer than $\stackrel{¯}{\mathrm{SP}}$. Find$ST$ and $SP$.

Quadrilateral ABCD is a parallelogram. Name the principal theorem or definition that justifies the statement.

$\stackrel{¯}{AD}â‰\dots \stackrel{¯}{BC}$

Quad. SLTM is a rhombus.

If$\mathbf{m}∠\mathbf{1}\mathbf{=}\mathbf{3}\mathbf{x}\mathbf{+}\mathbf{8}$ and$\mathbf{m}∠\mathbf{2}\mathbf{=}\mathbf{11}\mathbf{x}\mathbf{-}\mathbf{24}$ find the value of x.

Given: CDEF is a parallelogram; S and T are the midpoints of $\stackrel{¯}{\mathit{E}\mathit{F}}$and $\stackrel{¯}{\mathit{E}\mathit{D}}$.

Prove: $\stackrel{¯}{\mathit{S}\mathit{R}}â‰\dots \stackrel{¯}{\mathit{F}\mathit{D}}$.

Complete the following statements:

a. If a point lies on the perpendicular bisector of$\stackrel{¯}{AB}$, then the point is equidistant from ___?

b. If a point lies on the bisector of$∠RST$,then the point is equidistant from ___?

For the following figure, can you deduce from the information $∠ADCâ‰\dots ∠CBA$ and$∠BADâ‰\dots ∠DCB$ that quadrilateral ABCD is a parallelogram. If so, what theorem can you use?

Give the most descriptive name for quadrilateral MNOP.

$\stackrel{¯}{\mathit{M}\mathit{N}}â‰\dots \stackrel{¯}{\mathit{P}\mathit{O}};\stackrel{¯}{\mathit{M}\mathit{N}}âˆ\yen \stackrel{¯}{\mathit{P}\mathit{O}}$

The pliers shown are made in such a way that the jaws are always parallel. Explain.