91Ó°ÊÓ

Describe your plan for proving the following.

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

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

Find the value of $\mathbf{x}$.

With proofs in two-column form

Given: $\stackrel{\mathbf{¯}}{\mathbf{E}\mathbf{F}}\mathbf{âŠ\yen }\stackrel{\mathbf{¯}}{\mathbf{E}\mathbf{G}}\mathbf{\text{ }}\mathbf{;}\mathbf{\text{ }}\stackrel{\mathbf{¯}}{\mathbf{H}\mathbf{G}}\mathbf{âŠ\yen }\stackrel{\mathbf{¯}}{\mathbf{E}\mathbf{G}}$

$\stackrel{\mathbf{¯}}{\mathbf{E}\mathbf{H}}\mathbf{â‰\dots }\stackrel{\mathbf{¯}}{\mathbf{G}\mathbf{F}}$

Prove:$\mathbf{∠}\mathit{H}\mathbf{â‰\dots }\mathbf{∠}\mathit{F}$

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:$∠\mathbf{3}â‰\dots ∠\mathbf{4}$

Key steps of proof:

a. width="109" height="20" role="math">ΔLOB≅ΔJOB

b.$∠\mathbf{1}â‰\dots ∠\mathbf{2}$

c.$\mathrm{Δ}\mathbf{LBA}â‰\dots \mathrm{Δ}\mathbf{JBA}$

d.$∠\mathbf{3}â‰\dots ∠\mathbf{4}$

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

$\stackrel{\mathit{↔}}{\mathit{\text{BD}}}$bisects $∠\mathit{\text{ABC}}$,$\mathit{\text{m}}∠\mathit{\text{ABC}}\text{=}5\mathit{\text{x}}−4$and $\mathit{\text{m}}∠\mathit{\text{CBD}}\text{=}2\mathit{\text{x}}+10$. $∠\mathit{\text{ABC}}$is a(n) ________ angle.

For the following figure, if $\mathrm{Δ}AOD$is isosceles right triangle with right $∠AOD$then the measure of$∠A$is __?

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

$BI=\_\_$

In Exercises 28-33 xrepresents the length of a segment. When a value of xdoesn't make sense as a length, eliminate that value of x.

$x^2−17x+72=0$

Given:$\mathrm{Δ}\mathbf{ABC}$ in plane M; D not in plane M;

$∠\mathbf{ACB}â‰\dots ∠\mathbf{ABC};∠\mathbf{DCB}â‰\dots ∠\mathbf{DBC}$

Name a pair of congruent triangles. Prove that your answer is correct.