We are also given a statement about the congruence of the given triangles.
△DFG≅△HJK
We want to decide whether the congruence statement is true. To do so, we will consider the congruent sides of these triangles. Examining the diagram in the exercise, we can see that the two triangles have three congruent corresponding sides. Let's list these corresponding sides.
Congruent Sides [0.5em]
DF≅HJ
FG≅JK
DG≅HK
From here we can use the Side-Side-Side Congruence Theorem to show that â–³ DFG is congruent to â–³ HJK. Let's recall the theorem.
Side-Side-Side Congruence Theorem
If the three sides of a triangle are congruent to the three sides of another triangle, then the triangles are congruent.
Since we know that the three sides of â–³ DFG are congruent to the three sides of â–³ HJK, we have enough information to claim that these triangles are congruent by the Side-Side-Side Congruence Theorem.
DF≅HJ FG≅JK DG≅HK ⇒ △DFG≅△HJK
