91Ó°ÊÓ

Given: $\stackrel{¯}{\text{FC}}$ and $\stackrel{¯}{\text{SH}}$ bisect each other at $\text{A;}$localid="1638250328146" $\text{FC}=\text{SH}$.

Prove: $\text{SA}=\text{AC}$.

Suppose that $\mathrm{Δ}BIGâ‰\dots \mathrm{Δ}CAT$, then complete the following statement.

$\_\_\_=m∠A$

Given: $â–³\mathbf{MPQ}â‰\dots â–³\mathbf{PMN}$; $\stackrel{¯}{\mathrm{MS}}â‰\dots \stackrel{¯}{\mathrm{PR}}$.

Prove: $â–³\mathbf{MSN}â‰\dots â–³\mathbf{PRQ}$.

In Exercises 1-6 you are given a diagram that is marked with given information. Give the reason for each key step of the proof.

Prove:$\stackrel{¯}{\mathrm{BE}}â‰\dots \stackrel{¯}{\mathrm{DF}}$

Key steps of proof:

a. width="112" height="20" role="math">ΔABC≅ΔCDA

b.$∠\mathbf{1}â‰\dots ∠\mathbf{2}$

c.$\mathrm{Δ}\mathbf{ABE}â‰\dots \mathrm{Δ}\mathbf{CDF}$

d.$\stackrel{¯}{\mathrm{BE}}â‰\dots \stackrel{¯}{\mathrm{DF}}$

Given: $\mathit{Δ}\mathit{K}\mathit{O}\mathit{P}\mathbf{â‰\dots }\mathit{Δ}\mathit{M}\mathit{A}\mathit{T}$

Name three pairs of corresponding sides.

Complete the following statement with the word always, sometimes, or never.

Two isosceles triangles with congruent bases are ___ congruent.

For the following figure, state which congruence method can be used to prove the triangle congruent. If no method applies, say none.

Complete each sentence with the most appropriate word, phrase or value.

If two parallel planes are cut by a third plane, then the lines of intersection are ________.

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 $x=\frac{−bÂ\pm \sqrt{b^2−4ac}}{2a}$.

$n^2−6n+8=0$

In Exercises 1-3 you are given a diagram that is marked with given information. Give the reason for each key step of the proof.

Prove: $\stackrel{¯}{\mathrm{AX}}â‰\dots \stackrel{¯}{\mathrm{AY}}$

Key steps of proof:

a. $\mathrm{Δ}\mathbf{PAL}â‰\dots \mathrm{Δ}\mathbf{KAN}$

b. $∠\mathbf{L}â‰\dots ∠\mathbf{N}$

c. $\mathrm{Δ}\mathbf{LAX}â‰\dots \mathrm{Δ}\mathbf{NAY}$

d. $\stackrel{¯}{\mathrm{AX}}â‰\dots \stackrel{¯}{\mathrm{AY}}$