SOLUTION: Given: Triangle WXZ is isoceles. Point Y is the midpoint of segment XZ. Prove: Segment YW bisects Angle XWZ. There are 2 triangles. The whole Triangle is WXZ. Point W i

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Question 175914: Given: Triangle WXZ is isoceles. Point Y is the midpoint of segment XZ.
Prove: Segment YW bisects Angle XWZ.
There are 2 triangles. The whole Triangle is WXZ. Point W is at the top of the triangle and X is on the left corner and Z is on the right. Point Y is in between Points X and Z. Angles 1 and 2 are and the top of the triangle and 3 and 4 are at the bottom (Angle 1 is ANGLE WXY and Angle 2 is WYZ.) (Angle 3 is ANGLE WYX, and Angle 4 is ANGLE WYZ. Hope i was specific enough, and please help me. THANK YOU.
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
I'm assuming that the drawing looks like this (minus the labels of angles 1, 2, 3, and 4) Note: drawing is not to scale

Here's a two column proof:

Statement Reason
1. Triangle WXZ is isoceles Given

2. Point Y is the midpoint of segment XZE Given

3. Segment WX = Segment WZ Definition of Isosceles

4. Angle WXY = Angle WZY Definition of Isosceles

5. Segment XY = Segment YZ Definition of Midpoint

6. Triangle WXY = Triangle WYZ SAS Property of Congruence

7. Angle XWY = Angle YWZ CPCTC

8. Segment YW bisects Angle XWZ Definition of Angle Bisector

Note: CPCTC = Corresponding Parts of Congruent Triangles are Congruent

Remember, the definition of an isosceles triangle is that the triangle has two equal sides and two equal base angles. Also, remember that if two angles are equal, and they form a larger angle, this means that they are the result of a angle bisection.