91Ó°ÊÓ

Suppose you know that $\stackrel{¯}{DB}âŠ\yen \stackrel{¯}{DC}.$Explain how you can deduce that $\stackrel{¯}{DB}âŠ\yen \stackrel{¯}{BA}.$

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?

Find the measure of each numbered angle.

Given:$\stackrel{¯}{WX}âŠ\yen \stackrel{¯}{YZ};∠1â‰\dots ∠2;\stackrel{¯}{UX}â‰\dots \stackrel{¯}{VX}$

Which one(s) of the following statements must be true?

(1)$\stackrel{¯}{XW}âŠ\yen \stackrel{¯}{UV}$

(2)$\stackrel{¯}{UV}âˆ\yen \stackrel{¯}{YZ}$

(3)$\stackrel{¯}{VX}âŠ\yen \stackrel{¯}{UX}$

Plane M is the perpendicular bisecting plane of $\stackrel{\mathbf{¯}}{\mathit{A}\mathit{B}}$ at O (that is, M is the plane that is perpendicular to $\stackrel{\mathbf{¯}}{\mathit{A}\mathit{B}}$ at its midpoint, O). Points C and D also lie in plane M. List three pairs of congruent triangles and tell which congruence method can be used to prove each pair congruent.

Explain how corollary 3 follows from theorem 4-1.

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

$y^2-6y+9=0$

Given that $\stackrel{\mathbf{¯}}{\mathbf{B}\mathbf{C}}\mathbf{â‰\dots }\stackrel{\mathbf{¯}}{\mathbf{C}\mathbf{D}}\mathbf{,}\mathbf{}\stackrel{\mathbf{¯}}{\mathbf{B}\mathbf{D}}\mathbf{â‰\dots }\stackrel{\mathbf{¯}}{\mathbf{C}\mathbf{E}}$then prove that$\mathbf{Δ}\mathit{A}\mathit{B}\mathit{C}$is isosceles.

The two triangles shown are congruent. Complete.

a. $\mathrm{Δ}PALâ‰\dots$? .

b. $\stackrel{¯}{PA}â‰\dots$?.

c. $∠\mathbf{1}â‰\dots$? because ? .

Then $\stackrel{¯}{PA}âˆ\yen \underset{¯}{?}$ because ?.

d. $∠\mathbf{2}â‰\dots \underset{¯}{?}$ because ?.

Then $\underset{¯}{?}âˆ\yen \underset{¯}{?}$ because ?.

Can two triangles be proved congruent? If so, by which method, SSS, SAS, ASA, AAS, or HL?