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.

For the following figure, does the SAS postulates justify that the two triangles are congruent.

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

Write proof in two-column form.

Given: $\stackrel{¯}{\text{AD}}âŠ\yen \stackrel{¯}{\text{BC}}$; $\stackrel{¯}{\text{BA}}âŠ\yen \stackrel{¯}{\text{AC}}.$

Prove: $∠\mathbf{1}â‰\dots ∠\mathbf{2}\mathbf{.}$

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

$∠Gâ‰\dots \_\_$

Supply the missing statements and reasons.

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

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

If$\mathrm{Δ}AOD$ is isosceles, with $\stackrel{¯}{OA}â‰\dots \stackrel{¯}{OD}$. Then$∠\_\_â‰\dots ∠\_\_$?

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:$\stackrel{¯}{\mathrm{NE}}â‰\dots \stackrel{¯}{\mathrm{OS}}$

Key steps of proof:

a.$\mathrm{Δ}\mathbf{RNX}â‰\dots \mathrm{Δ}\mathbf{LOY}$

b.$∠\mathbf{X}â‰\dots ∠\mathbf{Y}$

c.$\mathrm{Δ}\mathbf{NEX}â‰\dots \mathrm{Δ}\mathbf{OSY}$

d.$\stackrel{¯}{\mathrm{NE}}â‰\dots \stackrel{¯}{\mathrm{OS}}$

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.

a.$\mathrm{Δ}\mathbf{ABC}â‰\dots \mathrm{Δ}\mathbf{DEF}$

b.$∠\mathbf{C}â‰\dots ∠\mathbf{F}$

c.$\mathrm{Δ}\mathbf{ACS}â‰\dots \mathrm{Δ}\mathbf{DFT}$

d.$\stackrel{¯}{\mathrm{AS}}â‰\dots \stackrel{¯}{\mathrm{DT}}$