91Ó°ÊÓ

Write proofs in two-column form.

Given: $\stackrel{¯}{\mathbf{GH}}âŠ\yen \stackrel{¯}{\mathbf{HJ}}$; $\stackrel{¯}{\mathbf{KJ}}âŠ\yen \stackrel{¯}{\mathbf{HJ}}$; $∠\mathbf{G}â‰\dots ∠\mathbf{K}$

Prove:$â–\mu \mathbf{GHJ}â‰\dots â–\mu \mathbf{KJH}$

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

$v^2+25=10v$

A young tree on level ground is supported at P by three wires of equal length. The wires are staked to the ground at points A, B, and C, which are equally distant from the base of the tree, T. Explain in a paragraph how you can prove that the angles the wires make with the ground are all congruent.

Given: $\stackrel{¯}{\mathrm{AM}}â‰\dots \stackrel{¯}{\mathrm{MB}};\stackrel{¯}{\mathrm{AD}}â‰\dots \stackrel{¯}{\mathrm{BC}}$

$∠\mathbf{MDC}â‰\dots ∠\mathbf{MCD}$

Prove: $\stackrel{¯}{\mathrm{AC}}≃\stackrel{¯}{\mathrm{BD}}$

The pentagons shown are congruent. Complete.

$\mathrm{KB}=\underset{¯}{?}\mathbf{cm}$

Plot the given points on graph paper. Draw $\mathrm{Δ}\mathit{\text{ABC}}$and $\mathrm{Δ}\mathit{\text{DEF}}$. Copy and complete the statement $\mathrm{Δ}\mathit{\text{ABC}}â‰\dots \underset{¯}{?}$.

$\mathit{\text{A}}\left(−7,−3\right)$$\mathit{\text{B}}\left(−2,−3\right)$$\mathit{\text{C}}\left(−\mathbf{2},0\right)$

$\mathit{\text{D}}\left(0,\mathbf{1}\right)$$\mathit{\text{E}}\left(5\text{,}\mathbf{1}\right)$$\mathit{\text{F}}\left(\mathbf{0},−2\right)$

Given:$\stackrel{¯}{\mathrm{PQ}}â‰\dots \stackrel{¯}{\mathrm{PR}}\mathbf{;}\mathbf{}\stackrel{¯}{\mathrm{TR}}â‰\dots \stackrel{¯}{\mathrm{TS}}$

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

(1)$\stackrel{¯}{\mathrm{ST}}\mathbf{\left|}\mathbf{\right|}\stackrel{¯}{\mathrm{QP}}$

(2)$\stackrel{¯}{\mathrm{ST}}â‰\dots \stackrel{¯}{\mathrm{QP}}$

(3)$∠\mathbf{T}â‰\dots ∠\mathbf{P}$

Write the proofs in two-column form.

Given: $∠\mathbf{1}â‰\dots ∠\mathbf{2}â‰\dots ∠\mathbf{3}$;$\stackrel{¯}{\mathrm{EN}}â‰\dots \stackrel{¯}{\mathrm{DG}}$

Prove: $∠\mathbf{4}â‰\dots ∠\mathbf{5}$

Use the diagrams on pages 153 and 154 to prove the following theorems.

15. Theorem 4-6

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.