Based on the given information, we can prove that ΔABC ≅ ΔDEF: A. yes; ABC ≅ DEF by the ASA Congruence Theorem.
In Eucldiean Geometry, two triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.
ASA is an abbreviation for Angle-Side-Angle and it states that when two (2) angles and their included side in two triangles are congruent, then the triangles are said to be congruent.
Based on the angle, side, angle (ASA) similarity theorem, we can logically deduce that triangle ABC and triangle DEF are both congruent based on the following reasons;
∠C ≅ ∠F
AB ≅ DE
BC ≅ EF
ΔABC ≅ ΔDEF
Complete Question:
Decide whether you can use the given information to prove that ΔABC ≅ ΔDEF. Explain your reasoning. ∠C ≅ ∠F, AB ≅ DE, BC ≅ EF.
yes; ΔABC ≅ ΔDEF by the ASA Congruence Theorem.
yes; ΔABC ≅ ΔDEF by the AAS Congruence Theorem.
no; The congruence statements follow the pattern SSA.
no; BC and EF are not corresponding sides.