Question

use the given information to prove that $df = gj$.
given: $de = hj$
$ef = gh$
prove: $df = gj$
1 $de = hj$ given
2 $ef = gh$ given
3 $df = gj$ symmetric property
validate

Explanation:

Step1: Use segment addition postulate

By segment addition postulate, \(DF = DE+EF\) and \(GJ=GH + HJ\).

Step2: Substitute using given equalities

Since \(DE = HJ\) (given) and \(EF = GH\) (given), substitute these into the equations from Step1. So \(DF=HJ + GH\) and \(GJ=GH + HJ\).

Step3: Use commutative property of addition

By commutative property of addition \(a + b=b + a\). Here \(HJ + GH=GH + HJ\). So \(DF = GJ\).

Answer:

\(DF = GJ\) is proved as shown above.