91Ó°ÊÓ

Supply the missing statements and reasons.

Given: $\stackrel{¯}{RS}âŠ\yen \stackrel{\mathit{¯}}{ST}$;$\stackrel{\mathit{¯}}{TU}âŠ\yen \stackrel{\mathit{¯}}{ST}$; is the midpoint of $\stackrel{¯}{ST}$.

Prove: $â–³RSVâ‰\dots â–³UTV$

Use the diagrams on pages 153 and 154 to prove the following theorems.

Theorem 4-8

Solve each equation by factoring or by using the quadratic formula. The quadratic formula is:

If $a{x}^2+bx+c=0$, with $a≠0$, then $x=\frac{-bÂ\pm \sqrt{b^2-4ac}}{2a}$.

$y^2=20y-36$

$\stackrel{¯}{WX}$and $\stackrel{¯}{YZ}$are perpendicular bisectors of each other.

How many pairs of congruent triangles are shown in the diagram?

Refer to $\mathrm{Δ}\mathbf{DEF}$ and name each of the following:

a. An altitude.

b. A median

c. The perpendicular bisector of a side of the triangle.

State whether the given information be used to prove that two lines are parallel and also state which lines.

Write a paragraph proof: If $\stackrel{¯}{\text{AX}}$is both a median and an altitude of $\mathrm{Δ}\text{ABC}$, then $\mathrm{Δ}\text{ABC}$ is isosceles.

For exercises 16-19 draw and label a diagram. List in terms of the diagram, what is given and what is to be proved. Then write a two column proof.

If$∠\mathbf{A}$ and$∠\mathbf{B}$ are the base angles of isosceles $â–³\mathit{A}\mathit{B}\mathit{C}$, and the bisector of$∠\mathbf{A}$ meets$\stackrel{¯}{\mathrm{BC}}$ at$X$ and the bisector of$∠\mathit{B}$ meets$\stackrel{¯}{\mathrm{AC}}$ at $Y$, then $\stackrel{¯}{\mathrm{AX}}â‰\dots \stackrel{¯}{\mathrm{BY}}$.

Write proofs in two–column form.

Given:$\stackrel{¯}{\mathrm{XY}}â‰\dots \stackrel{¯}{\mathrm{XZ}}\mathbf{;}$

$\stackrel{¯}{\mathrm{YO}}$bisects$∠\mathbf{XYZ}$

$\stackrel{¯}{\mathrm{ZO}}$bisects$∠\mathbf{XZY}$

Prove: $\stackrel{¯}{\mathrm{YO}}â‰\dots \stackrel{¯}{\mathrm{ZO}}$

Plot the given points on graph paper. Draw $\mathrm{Δ}\mathit{\text{ABC}}$and $\stackrel{\mathit{¯}}{\mathit{\text{DE}}}$. Find two locations of point$\mathit{\text{F}}$ such that$\mathrm{Δ}\mathit{\text{ABC}}â‰\dots \mathrm{Δ}\mathit{\text{DEF}}$.

1. Name the coordinates of points A, B, and C.
2. Name the coordinates of a point D such that$\mathrm{Δ}ABCâ‰\dots \mathrm{Δ}ABD$.