91Ó°ÊÓ

Decide whether you can deduce by the SSS, SAS, or ASA postulate that another triangle is congruent to $\mathrm{Δ}ABC$. If so, write the congruence and name the postulate used. If not, write no congruence can be deduced.

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

Two isosceles tringles with congruent vertex angles are ___ congruent.

Draw a right triangle. Then draw its three altitudes in color.

In $â–³\mathbf{JKL}$name each of the following.

a. an altitude

b. a median

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

$y^2−7y−18=0$

In the following figure, the two-triangle shown are congruent. Then complete the following statement.

$∠Râ‰\dots ∠\_\_\_$

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: $∠\mathbf{G}â‰\dots ∠\mathbf{T}$

Key steps of proof:

a.$\mathrm{Δ}\mathbf{RAJ}â‰\dots \mathrm{Δ}\mathbf{NAK}$

b.$\stackrel{¯}{\mathrm{RJ}}â‰\dots \stackrel{¯}{\mathrm{NK}}$

c.$\mathrm{Δ}\mathbf{GRJ}â‰\dots \mathrm{Δ}\mathbf{TNK}$

d.$∠\mathbf{G}â‰\dots ∠\mathbf{T}$

Complete.

If $\mathit{K}$is the midpoint of $\stackrel{\mathbf{¯}}{\mathit{S}\mathit{T}}$and $\stackrel{\mathbf{¯}}{\mathit{R}\mathit{K}}\mathbf{âŠ\yen }\stackrel{\mathbf{¯}}{\mathit{S}\mathit{T}}$, then $\stackrel{\mathbf{¯}}{\mathit{R}\mathit{K}}$is called $\mathit{a}\mathbf{\left(}\mathit{n}\mathbf{\right)}\underset{\mathbf{¯}}{\mathbf{?}}$of $\stackrel{\mathbf{¯}}{\mathit{S}\mathit{T}}$

Write proofs in two–column form.

3. Given: $\stackrel{\mathbf{¯}}{\mathbf{W}\mathbf{O}}\mathbf{â‰\dots }\stackrel{\mathbf{¯}}{\mathbf{Z}\mathbf{O}}\mathbf{;}\stackrel{\mathbf{¯}}{\mathbf{X}\mathbf{O}}\mathbf{â‰\dots }\stackrel{\mathbf{¯}}{\mathbf{Y}\mathbf{O}}$

Prove: $\mathbf{∠}\mathit{W}\mathbf{â‰\dots }\mathbf{∠}\mathit{Z}$

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.