91Ó°ÊÓ

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$x=\frac{−bÂ\pm \sqrt{b^2−4ac}}{2a}$.

$y^2=13y$

For the following figure, given the two congruent angles$∠1â‰\dots ∠2$. Name two segments that must be congruent.

For the following figure, find the value of $x$.

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

$\mathrm{Δ}IGBâ‰\dots \_\_$

Decide whether the two triangles must be congruent. If so, write the congruence and name the postulate used. If not, write no congruence can be deduced.

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:$\stackrel{¯}{\mathrm{DX}}â‰\dots \stackrel{¯}{\mathrm{EX}}$

Key steps of proof:

a.$\mathrm{Δ}\mathbf{POD}â‰\dots \mathrm{Δ}\mathbf{POE}$

b.$\stackrel{¯}{\mathrm{PD}}â‰\dots \stackrel{¯}{\mathrm{PE}}$

c.$\mathrm{Δ}\mathbf{PDX}â‰\dots \mathrm{Δ}\mathbf{PEX}$

d.$\stackrel{¯}{\mathrm{DX}}â‰\dots \stackrel{¯}{\mathrm{EX}}$

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

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.

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

$∠Aâ‰\dots ∠\_\_\_$

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