Question

In triangle ABC and triangle DEF, AB=DE, angle A=angleD and AC=DF. Are

the triangles congruent? If yes , by which congruence rule?​

Answer 1

Question:

In triangle ABC and triangle DEF, AB=DE, ∠A=∠D and AC=DF. Are

the triangles congruent? If yes , by which congruence rule?​

Given:

• AB = DE

• ∠A = ∠D

• AC = DF

$\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\thicklines\qbezier(1, 0)(1,0)(3,3)\qbezier(5,0)(5,0)(3,3)\qbezier(5,0)(1,0)(1,0)\put(2.85,3.2){ \bf A }\put(0.5,-0.3){ \bf C }\put(5.2,-0.3){ \bf B }\end{picture}$

$\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\thicklines\qbezier(1, 0)(1,0)(3,3)\qbezier(5,0)(5,0)(3,3)\qbezier(5,0)(1,0)(1,0)\put(2.85,3.2){ \bf D }\put(0.5,-0.3){ \bf F }\put(5.2,-0.3){ \bf E }\end{picture}$

To Prove:

Whether ΔABC ≅ ΔDEF or not

Solution:

Given In ΔABC and  ΔDEF

• AB = DE ( Given ) - Side

• ∠A = ∠D( Given ) - Angle

• AC = DF  ( Given ) - Side

By SAS Congruency criterion

ΔABC ≅ ΔDEF

Answer:

Yes the triangles are congruent By SAS Congruency criterion

ΔABC ≅ ΔDEF