Question

Hi! Currently struggling with understanding this.

I need an explanation and step process please!
Thank you so much (-:

Answer 1

Therefore the length FG is 16 unit.

Explanation:

Given:

∠E ≅ ∠G = 90°

DF bisects ∠EDG

Bisector Divide the angle in EQUAL parts

∴∠EDF ≅ ∠GDF

FE = n +5

FG = 2n - 6

To Find:

FG = ?

Solution:

In ΔEDF and ΔGDF

∠E ≅ ∠G = 90° ……….{Given}

∠EDF ≅ ∠GDF ..……..{DF bisects ∠EDG}

DF ≅ DF ……….{Reflexive Property}

ΔEDF ≅ ΔGDF ….{ By Angle-Angle-Side Congruence test}

∴ FE ≅ FG .....{corresponding parts of congruent triangles are congruent}

Substituting the values of FE and FG we get

`n+5=2n-6\\2n-n=5+6\\n=11`

Substituting ' n ' in FG we get

`FG=2* 11-6=22-6=16\ unit\\FG =16\ unit`

Therefore the length FG is 16 unit.