Question

17.) DF bisects (3 points)

Answer 1

Answer:

Therefore,

$EF=16\ unit\\GF=16\ unit$

Step-by-step 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

$EF = 11 +5=16\ unit\\GF = 2\times 11 - 6=22-11=16$

Therefore,

$EF=16\ unit\\GF=16\ unit$