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.

Suppose that $\mathrm{Δ}FINâ‰\dots \mathrm{Δ}WEB$name the three pairs of corresponding sides.

Supply the missing statements and reasons.

Given: $∠\mathbf{W}$and $∠\mathbf{Y}$are right angles; $\stackrel{¯}{\mathrm{WX}}â‰\dots \stackrel{¯}{\mathrm{YX}}$

Prove:$\stackrel{¯}{\mathrm{WZ}}â‰\dots \stackrel{¯}{\mathrm{YZ}}$

a. Draw a large scalene triangle $\mathbf{ABC}$. Carefully draw the bisector of $∠\mathbf{A}$, the altitude from $\mathbf{A}$, and the median from $\mathbf{A}$. These three should all be different.

b. Draw a large isosceles triangle $\mathbf{ABC}$with vertex angle $\mathbf{A}$. Carefully draw the bisector of $∠\mathbf{A}$, the altitude from $\mathbf{A}$, and the median from $\mathbf{A}$. Are these three different?

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

Write the Isosceles triangle theorem and its converse as a single biconditional statement.

The two triangles shown are congruent. Complete.

a. $\mathrm{Δ}STOâ‰\dots$? .

b. $∠Sâ‰\dots$? because ?.

c. $∠SOâ‰\dots$? because ? .

Then point O is the midpoint of? .

d. $∠Tâ‰\dots$? because ?.

Then $\stackrel{¯}{ST}âˆ\yen \stackrel{¯}{RK}$because ?.

Find the measure of each numbered angle.

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.

Tell which pairs of congruent parts and what methods $\mathbf{(}\mathit{S}\mathit{S}\mathit{S}\mathbf{,}\mathbf{}\mathit{S}\mathit{A}\mathit{S}\mathbf{,}\mathbf{}\mathit{A}\mathit{S}\mathit{A}\mathbf{,}\mathbf{}\mathit{A}\mathit{A}\mathit{S}\mathbf{,}\mathbf{}\mathbf{or}\mathbf{}\mathit{H}\mathit{L}\mathbf{)}$you would use to prove the triangles are congruent.

Given: $∠\mathbf{1}â‰\dots ∠\mathbf{2}\mathbf{;}\mathbf{}\mathbf{∠}\mathbf{3}\mathbf{â‰\dots }\mathbf{∠}\mathbf{4}\mathbf{;}\mathbf{}\stackrel{\mathbf{¯}}{\mathrm{QR}}\mathbf{â‰\dots }\stackrel{\mathbf{¯}}{\mathrm{TS}}$

$\mathbf{â–³}\mathbf{QPR}\mathbf{â‰\dots }\mathbf{â–³}\mathbf{TPS}$by what method?