SOLUTION: ISBN 0- 13- 062560- 4 Given: X is the midpoint of line AG and of line NR Prove: triangle ANX is congruent to triangle GRX

Question 160862: ISBN 0- 13- 062560- 4
Given: X is the midpoint of line AG and of line NR
Prove: triangle ANX is congruent to triangle GRX
Answer by gonzo(654) (Show Source): You can put this solution on YOUR website!
if i understand you correctly, they are congruent by SAS as follows:
x must be the intersection of NR and AG since it is common to both.
since it is the midpoint of both, then NX = XR, and AX = XG
to complete the triangles, we connect point A to point N, and we connect point R to point G (any 2 points define a line).
we have 2 triangles that are on opposite sides of point X so that angle AXN is vertical angle to angle RXG. since vertical (opposite) angles created by 2 intersecting lines are equal, angle AXN is equal to angle RXG.
the SAS proof of congruency is determined as follows:
angle AXN in triangle AXN is congruent to angle RXG in triangle RXG (vertical angles)
AX in triangle AXN is congruent to XG in triangle RXG (midpoint X of line AG created these).
NX in triangle AXN is congruent to XR in triangle RXG (midpoint X of line NR created these).
triangles are congruent by SAS. this means they have two correscponding sides that are congruent and the angle between those 2 corresponding sides is congruent also.

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