Conventions to Express Congruence

Transcript

Conventions to Express CongruenceGiven these two triangles are congruent How can these two triangles be superimposed? Which vertices of ∆XYZ and ∆ABC should we overlap? We see that AC = XZ AB = XY BC = YZ So, As AC = XZ, Point A can overlap Point X or Point Z Also, AB = XY, since Point X occurs in both cases Point A overlaps with point X So, we can say C overlaps with Z And, B overlaps with Y Let’s check this by actually super-imposing So, Points match A ⟷ X B ⟷ Y C ⟷ Z Thus, we write ∆ABC ≅ ∆XYZ Now, It is not correct to write ∆ ABC ≅ ∆ YXZ or ∆ ABC ≅ ∆ ZXY It is correct to write ∆ BAC ≅ ∆ YXZ or ∆ CAB ≅ ∆ZXY And, we write it like But, why is this order important? Because of CPCT, CPCT is corresponding parts of Congruent Triangles If two triangles are congruent, Their corresponding sides are equal Their corresponding angles are equal Since ∆ABC ≅ ∆XYZ Then, Corresponding angles are equal Corresponding sides are equal