MATH SOLVE

6 months ago

Q:
# 10. Provide the reasons for the following proof:Given: Line WX =~ Line XY, Line XZ bisects Angle WXYProve: Triangle WXZ =~ Triangle YXZThe last answer choice is symmetric property of =~;SASAm I correct?

Accepted Solution

A:

Given that Line WX is congruent to Line XY and Line XZ bisects Angle WXY.

We prove that triangle WXZ is congruent to triangle YXZ as follows:

[tex]\begin{tabular} {|c|c|} Statement&Reason\\[1ex] \overline{WX}\cong\overline{XY},\ \overline{XZ}\ bisects\ \angle WXY&Given\\ \angle WXY\cong\angle YXZ & Deifinition of an angle bisector\\ \overline{XZ}\cong\overline{ZX}&Refrexive Property of \cong\\ \triangle WXZ\cong\triangle YXZ&SAS \end{tabular}[/tex]

We prove that triangle WXZ is congruent to triangle YXZ as follows:

[tex]\begin{tabular} {|c|c|} Statement&Reason\\[1ex] \overline{WX}\cong\overline{XY},\ \overline{XZ}\ bisects\ \angle WXY&Given\\ \angle WXY\cong\angle YXZ & Deifinition of an angle bisector\\ \overline{XZ}\cong\overline{ZX}&Refrexive Property of \cong\\ \triangle WXZ\cong\triangle YXZ&SAS \end{tabular}[/tex]