Question

Riangle ABC is isoscelesGJ bisects ∠FGH and is a perpendicular bisector of FH. Triangle F G H is cut by perpendicular bisector G J. Line segments F J and J H are congruent. Angle F G J and J G H are both 30 degrees. 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.

Answer 1

It has exactly 3 congruent sides

Explanation:

took the unit test on edg 2020

Answer 2

It has exactly 3 congruent sides.

Explanation:

Since ∠FGJ = ∠JGH = 30° and GJ is a perpendicular bisector of FH, ∠GJF = 90°. So in ΔFGJ, ∠FGJ + ∠GJF + ∠GFJ = 180°.

So, 30° + 90° + ∠GFJ = 180°

120° + ∠GFJ = 180°

∠GFJ = 180° - 120°

∠GFJ = 60°

Also, since GJ is the perpendicular bisector of FH, ∠GJH = 90°. So in ΔJGH, ∠JGH + ∠GJH + ∠JHG = 180°.

So, 30° + 90° + ∠JHG = 180°

120° + ∠JHG = 180°

∠JHG = 180° - 120°

∠JHG = 60°

Since ∠FGH = ∠FGJ + ∠JGH = 30° + 30° = 60°

Since ∠FGH = ∠GFJ = ∠JHG = 60°

So, ΔFGJ is an equilateral triangle. Since all its angles are equal, so also, all its sides are equal. So, ΔFGJ is congruent by SSS and AAA so its 3 sides are congruent.

So exactly 3 sides are congruent in ΔFGJ.