GJ bisects ∠FGH and is a perpendicular bisector of FH.



What is true of triangle FGH?

It is a right triangle.
It is an obtuse triangle.
It has exactly 2 congruent sides.
It has exactly 3 congruent sides.

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Solution:

In [tex]\Delta[/tex] FGH, As, given G J bisects ∠F G H and is a perpendicular bisector of F H.

So, F J=J H →→ G J is a perpendicular bisector of F H.

We will use angle bisector theorem to determine which statement is correct.

As, Angle bisector theorem states that , if a line segment bisects an angle, then the ratio of sides adjacent to angle, is equal to the ratio of two segments where the angle bisector cuts the third side.

So, [tex]\frac{GH}{GF}=\frac{HJ}{JF}\\\\ \frac{GH}{GF}=1\\\\ GH=GF[/tex]

The option (C) which is the  [tex]\Delta[/tex] F G H has exactly 2 congruent sides is true.

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Answer:

The correct answer would be It has exactly 3 congruent sides.

Step-by-step explanation:

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