Answer:
XG segment is an angle bisector of ∠YXZ ⇒ C
Step-by-step explanation:
Let us revise the steps of constructing a bisector of an angle
- Place compass pin on the vertex of the angle (point X).
- Open the compass to a suitable length that and draw an arc to intersect the two sides of the angle at two points (points E and F)
- Place the compass pin on one of these new points on the sides of the angle(point E). Stretch the compass to a sufficient length and draw an arc in the interior of the angel
- Without changing the span on the compass, place the pin of the compass on the other intersection point on the side of the angle (point F) and make a similar arc. The two small arcs in the interior of the angle are intersecting. in a point (point P)
- Join the vertex of the angle (point X) to this intersection of the two small arcs (point P) XP is the bisector of angle X
By comparing these steps with The steps in the figure, you will find that they are the same steps
∵ XP ray intersect YZ segment at G
∴ G belong to XP ray
∵ XP ray is the bisector of ∠YXZ
∴ XG segment is the bisector of ∠YXZ
Then the statement must be true is:
XG segment is an angle bisector of ∠YXZ
