Question

In triangle FGH, GJ is an angle bisector of ∠G and perpendicular to FH.



What is the length of FH?

Answer 1

What kind of triangles are FGJ and HGJ?

Answer 2

they're isosceles triangle

Answer 3

You're close.
Triangle FGH is isosceles.
What does that tell you about the lengths of sides FG and HG?

Answer 4

they are right triangles

Answer 5

so it would be 3x-8=90

Answer 6

Since GJ bisects angle G, angles FGJ and HGJ are congruent.
Segment GJ is congruent to itself.
Angles FJG and HJG are both right angles, so they are congruent.
That makes triangles FGJ and HGJ congruent by ASA.
Then sides GF and GH are congruent by CPCTC making triangle FGH isosceles.

Answer 7

We know that sides GF and GH are congruent.
That means their lengths are equal.

Answer 8

yes

Answer 9

90 is an angle measure.
3x + 8 is a side length.
We cannot mix those two together.

Answer 10

so can we add 16+90?

Answer 11

Where did 90 come from?

Answer 12

the angle measure

Answer 13

no but I forgot we cant add the side and angle measure

Answer 14

For the two congruent right triangles, we only know the measure of one pair of angles. It's the right angles. We don't know anything about any other angle measures.
The question is what is a side length. We are not concerned with angle measures.

Answer 15

okay

Answer 16

If we can find x, we can find the length of FH since the length of FH is twice x.

Answer 17

so its 2x?