91Ó°ÊÓ

In \(\Delta \mathrm{EFG}\) , the bisector of \(\angle \mathrm{F}\) intersects the bisector of \(\angle \mathrm{G}\) at point \(\mathrm{H}\) . Explain why \(\overline{\mathrm{FG}}\) must be longer than \(\overline{\mathrm{FH}}\) or \(\overline{\mathrm{HG}}\)

In Exercises \(19-22,\) write an equation of the perpendicular bisector of the segment with the given endpoints. $$ \mathrm{M}(1,5), \mathrm{N}(7,-1) $$

Describe the possible lengths of the third side of the triangle given the lengths of the other two sides. ( See Example 5.) $$25 \text { meters, } 25 \text { meters}$$

In Exercises \(19-22,\) write an equation of the perpendicular bisector of the segment with the given endpoints. $$ Q(-2,0), R(6,12) $$

In Exercises \(19-22\) , tell whether the orthocenter is inside, on, or outside the triangle. Then \(\square\) nd the coordinates of the orthocenter. (See Example 3 ) $$\mathrm{A}(-4,0), \mathrm{B}(1,0), \mathrm{C}(-1,3)$$

In Exercises \(19-22,\) write an equation of the perpendicular bisector of the segment with the given endpoints. $$ \mathrm{U}(-3,4), \mathrm{V}(9,8) $$

Is it possible to construct a triangle with the given side lengths? If not, explain why not. $$6,7,11$$

Is it possible to construct a triangle with the given side lengths? If not, explain why not. $$3,6,9$$

In Exercises \(19-22,\) write an equation of the perpendicular bisector of the segment with the given endpoints. $$ \mathrm{Y}(10,-7), \mathrm{Z}(-4,1) $$

Is it possible to construct a triangle with the given side lengths? If not, explain why not. $$28,17,46$$