91Ó°ÊÓ

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

$\mathrm{AX}=\frac{1}{2}\mathrm{AC}$

Give the most descriptive name for quadrilateral MNOP.

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

Quad. STLM is a rhombus.

If $\mathbf{m}∠\mathbf{1}\mathbf{=}\mathbf{3}\mathbf{x}\mathbf{+}\mathbf{1}$and $\mathbf{m}∠\mathbf{3}\mathbf{=}\mathbf{7}\mathbf{x}\mathbf{-}\mathbf{11}$find the value of x.

Prove Theorem $5-1$.

Prove Theorem $5-1$.

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

$\stackrel{↔}{\text{AE}},\stackrel{↔}{\text{BF}},\stackrel{↔}{\text{CG}}$and $\stackrel{↔}{\text{DH}}$are parallel, with $\text{EF}=\text{FG}=\text{GH}$. Complete.

If $\text{AC}=\mathbf{22}−\text{x}$ and $\text{BD}=\mathbf{3}\text{x}−\mathbf{22}$ then $\text{x}=$ ? .

For the following figure, can you deduce from the information $\stackrel{¯}{AD}\left|\right|\stackrel{¯}{BC}$ and$\stackrel{¯}{AD}â‰\dots \stackrel{¯}{BC}$ that quadrilateral ABCD is a parallelogram. If so, what theorem can you use?

Complete the following statements:

Suppose that$\mathrm{Δ}ARTâ‰\dots \mathrm{Δ}DEB$.

a. $\mathrm{Δ}EBDâ‰\dots \_\_$

b.$\stackrel{¯}{AT}â‰\dots \_\_$

c.$m∠R=\_\_$

$\stackrel{↔}{\text{AE}},\stackrel{↔}{\text{BF}},\stackrel{↔}{\text{CG}}$and $\stackrel{↔}{\text{DH}}$are parallel, with $\text{EF}=\text{FG}=\text{GH}$. Complete.

If $\text{AB}=\mathbf{15}$, $\text{BC}=\mathbf{2}\text{x}−\text{y}$and $\text{CD}=\text{x}+\text{y}$, then $\text{x}=$ ? and $\text{y}=$ ? .