91Ó°ÊÓ

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:$\stackrel{¯}{\mathrm{AL}}â‰\dots \stackrel{¯}{\mathrm{CM}}$

Key steps of proof:

a.$\mathrm{Δ}\mathbf{ABD}â‰\dots \mathrm{Δ}\mathbf{CDB}$

b. $\stackrel{¯}{\mathrm{AD}}â‰\dots \stackrel{¯}{\mathrm{CB}};∠\mathbf{1}â‰\dots ∠\mathbf{2}$

c.$\mathrm{Δ}\mathbf{ADL}â‰\dots \mathrm{Δ}\mathbf{CBM}$

d.$\stackrel{¯}{\mathrm{AL}}â‰\dots \stackrel{¯}{\mathrm{CM}}$

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

If two intersecting lines form congruent adjacent angles, then the lines are ________.

Complete.

A method that can be used to prove right triangles congruent, but cannot be used with other types of triangles, is the$\underset{\_}{?}$method.

Draw a large acute scalene triangle. Then draw the perpendicular bisectors of its three sides.

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

Two equilateral triangles with congruent bases are ___ congruent.

Note that $\mathit{Z}\mathit{L}\mathbf{=}\mathit{Z}\mathit{J}$. Can you deduce that$\mathit{K}\mathit{Z}$ bisects $∠\mathit{L}\mathit{K}\mathit{J}$?

Decide whether the two triangles must be congruent. If so, write the congruence and name the postulate used. If not, write no congruence can be deduced.

Write proofs in two–column form.

Given: $M$is the midpoint of $\stackrel{¯}{AB}$;$∠1â‰\dots ∠2;∠3â‰\dots ∠4$

Prove: $\stackrel{¯}{AC}â‰\dots \stackrel{¯}{BD}$

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$x=\frac{−bÂ\pm \sqrt{b^2−4ac}}{2a}$.

$x^2+8x=0$

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

$\_\_â‰\dots \stackrel{¯}{AT}$