91Ó°ÊÓ

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

$\stackrel{¯}{AO}â‰\dots \_\_\_$

For the following figure, can the triangle be proved congruent. If so, what postulate can be used?

For the following figure, given the two congruent angles$∠5â‰\dots ∠6$. Name two segments that must be congruent.

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

Use the information given in each exercise to name the method $\mathbf{(}\mathit{S}\mathit{A}\mathit{S}\mathbf{,}\mathbf{}\mathit{A}\mathit{A}\mathit{S}\mathbf{,}\mathbf{}\mathit{S}\mathit{S}\mathit{S}\mathbf{,}\mathbf{}\mathit{A}\mathit{S}\mathit{A}\mathbf{,}\mathbf{}\mathbf{or}\mathbf{}\mathit{H}\mathit{L}\mathbf{)}$ you could use to prove $\mathit{Δ}\mathbf{\text{ }}\mathit{A}\mathit{O}\mathit{B}\mathbf{â‰\dots }\mathit{Δ}\mathit{A}\mathit{O}\mathit{C}$.You need not write the proofs.

Given $\stackrel{\mathbf{¯}}{\mathbf{A}\mathbf{O}}\mathbf{âŠ\yen }\mathbf{\text{±è±ô²¹²Ô±ð }}\mathit{M}\mathbf{;}\mathbf{}\stackrel{\mathbf{¯}}{\mathbf{A}\mathbf{B}}\mathbf{â‰\dots }\stackrel{\mathbf{¯}}{\mathbf{A}\mathbf{C}}$

Draw a diagram for the following:

a. Acute scalene$\mathbf{Δ}\mathit{J}\mathit{K}\mathit{L}$.

b. obtuse scalene $\mathbf{Δ}\mathit{J}\mathit{K}\mathit{L}$.

Given:$\stackrel{¯}{\mathrm{LF}}â‰\dots \stackrel{¯}{\mathrm{KF}}\mathbf{;}\mathbf{}\stackrel{¯}{\mathrm{LA}}â‰\dots \stackrel{¯}{\mathrm{KA}}$

Prove:$\stackrel{¯}{\mathrm{LJ}}â‰\dots \stackrel{¯}{\mathrm{KJ}}$

a. List the key steps of a proof.

b. Write a proof in two-column form.

If $\mathrm{Δ}DEFâ‰\dots \mathrm{Δ}RST,m∠D=100$and $m∠F=40$. Name four congruent angles.

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

If the measure of each interior angle of a polygon is 144, then the polygon has ________ sides.

Complete.

Draw $\stackrel{¯}{XY}$. Label its midpoint $\mathit{Q}$.

a. Select a point $\mathit{P}$equidistance from$\mathit{X}$ and$\mathit{Y}$ Draw width="26" height="24" role="math">PX¯,$\stackrel{\mathbf{¯}}{\mathit{P}\mathit{Y}}$and$\stackrel{\mathbf{¯}}{\mathit{P}\mathit{Q}}$

b. What postulate justifies the statement $\mathbf{Δ}\mathit{P}\mathit{Q}\mathit{X}\mathbf{â‰\dots }\mathbf{Δ}\mathit{P}\mathit{Q}\mathit{Y}$?

c. What reason justifies the statement $\mathbf{∠}\mathit{P}\mathit{Q}\mathit{X}\mathbf{â‰\dots }\mathbf{∠}\mathit{P}\mathit{Q}\mathit{Y}$?

d. What reason justifies the statement width="70" height="24" role="math">PQ↔⊥XY¯?

e. What name forwidth="27" height="24" role="math">PQ↔ best describes the relationship betweenwidth="27" height="24" role="math">PQ↔ and width="26" height="24" role="math">XY¯?