djkingsten50
Answered

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How would you solve a problem like this

How Would You Solve A Problem Like This class=

Sagot :

Answer:

ΔGJH ≅ ΔEKF

HL: GH and EF

SAS: FK and JH (or GH and EF)

ASA: ∠JGH and ∠FEK (or ∠EFK and ∠JHG)

ΔGFJ ≅ ΔEKH

SSS: KH and FJ

SAS: ∠KEH and ∠FGJ

Step-by-step explanation:

List whatever angles/sides need to be congruent for the two triangles to be congruent.

Prove ΔGJH ≅ ΔEKF using....

- HL (Hypotenuse + Leg)

           We already have two legs that are congruent (EK and GJ), so we just need the hypotenuses (GH and EF) to be equal.

- SAS (Side + Angle + Side)

         1 pair of sides (EK and JG) are equal, and m∠EKF = m∠GJH. So we need one more side. You can either use FK and JH or GH and EF.

- ASA (Angle + Side + Angle)

         1 pair of angles (∠EKF and ∠GJH) are already given as equal, and 1 pair of sides (EK and GJ) are equal. We just need one more pair of angles. So either ∠JGH and ∠FEK or ∠EFK and ∠JHG.

Prove ΔGFJ ≅ ΔEKH using...

- SSS (Side + Side + Side)

          Two pairs of sides (EK + GJ and EH + FG) are equal, so KH and FJ need to be equal.

- SAS (Side + Angle + Side)

          FG + EH and KE + GJ are equal. We need to use the angle in between them to use SAS, so ∠KEH and ∠FGJ need to be equal.

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