Question

17.) DF bisects

(3 points)

Answer 1

Therefore,

`EF=16\ unit\\GF=16\ unit`

Explanation:

Given:

DF bisects ∠ EDG

EF = n +5

GF = 2n - 6

To Find:

GF =? or

EF =?

Solution:

In ΔDEF and ΔDGF

∠E ≅ ∠G ……….{Measure of each angle is 90° given}

∠EDF ≅ ∠GDF ………..{ DF bisects ∠ EDG }

DF ≅ DF ……….{Reflexive Property}

ΔDEF ≅ ΔDGF ….{ By Angle-Angle-Side Congruence Postulate}

∴ EF ≅ GF ..{Corresponding Parts of Congruent Triangles are Congruent }

Substituting the values we get

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

Substituting 'n' in EF and GF we get

`EF = 11 +5=16\ unit\\GF = 2* 11 - 6=22-11=16`

Therefore,

`EF=16\ unit\\GF=16\ unit`