91Ó°ÊÓ

In the diagram,$\mathbf{m}∠\mathbf{VOZ}\mathbf{=}\mathbf{90}$ .

$\stackrel{¯}{\mathrm{OW}}$is an altitude of$△\mathbf{VOZ}$ .

$\stackrel{¯}{\mathrm{OX}}$bisects $∠\mathbf{VOZ}$.

$\stackrel{¯}{\mathrm{OY}}$is a median of$△\mathbf{VOZ}$ .

Find the measures of the four numbered angles.

$\mathbf{m}∠\mathbf{Z}\mathbf{=}\mathbf{k}$

Draw a quadrilateral of the type named. Join, in order, the midpoints of the sides. What special kind of quadrilateral do you appear to get?

Carefully draw an isosceles trapezoid and measure its diagonal. What do you discover? Write proof of your discovery.

$\stackrel{¯}{\text{RA}}$is an altitude of $\mathrm{Δ}\text{SAT}$. Pand Q are midpoints of $\stackrel{¯}{\text{SA}}$and $\stackrel{¯}{\text{TA}}$. $\text{SR}=9$, $\text{RT}=16$, $\text{QT}=10$, and $\text{PR}=7.5$.

Find the perimeter of $\mathrm{Δ}\text{PQR}$.

$â–\pm \mathrm{DECK}$is a parallelogram. Complete.

If $\mathrm{DE}=\mathrm{x}+\mathrm{y},\mathrm{EC}=12,\mathrm{CK}=2\mathrm{x}-\mathrm{y}$and $\mathrm{KD}=3\mathrm{x}-2\mathrm{y}$then and $\mathrm{x}=?$,$\mathrm{y}=?$, and the perimeter of$â–\pm \mathrm{DECK}$

In exercises 26-29, complete each statement about the diagram. Then state the definition, postulate or theorem that justifies your answer.

If$\mathbf{LM}\mathbf{=}\mathbf{ON}$ and $\mathbf{LO}\mathbf{=}\mathbf{MN}$, then$\mathbf{LMNO}$ is a$\underset{\_}{?}$ .

$\stackrel{¯}{\text{RA}}$is an altitude of $\mathrm{Δ}\text{SAT}$. P and Q are midpoints of $\stackrel{¯}{\text{SA}}$and $\stackrel{¯}{\text{TA}}$. $\text{SR}=9,\text{RT}=16,\text{QT}=10,$and $\text{PR}=7.5$

Find the perimeter of $\mathrm{Δ}\text{SAT}$.

$â–\pm \mathrm{DECK}$is a parallelogram. Complete.

If$\mathrm{m}∠1=3\mathrm{x},\mathrm{m}∠2=4\mathrm{x}$ and $\mathrm{m}∠3={\mathrm{x}}^2-70$then $\mathrm{x}=?$and$\mathrm{m}∠\mathrm{CED}=?$ (numerical answers).

Prove that the base angles of an isosceles trapezoid are congruent.

In exercises 26-29, complete each statement about the diagram. Then state the definition, postulate or theorem that justifies your answer.

If$\mathbf{LMNO}$ is a rhombus , then$∠\mathbf{LOM}â‰\dots \underset{\_}{?}â‰\dots \underset{\_}{?}â‰\dots \underset{\_}{?}$ .

Given: $â–\pm \text{ABZY}$; $\stackrel{¯}{\text{ZY}}â‰\dots \stackrel{¯}{\text{BX}}$; $∠1â‰\dots ∠2$

Prove: ABZY is a rhombus.