Match each set of conditions with the corresponding relationship between ∆abc and ∆xyz and the criterion (if any) that proves th
e relationship. tiles ab = xy, bc = yz, and angle b is congruent to angle y. ∆abc and ∆xyz are congruent by the sss criterion. ab = xy, and angles a and b are congruent to angles x and y, respectively. ∆abc and ∆xyz are not necessarily congruent. angles a, b, and c are congruent to angles x, y, and z, respectively. ∆abc and ∆xyz are congruent by the sas criterion. ab = xy, bc = yz, and ca = zx. ∆abc and ∆xyz are congruent by the asa criterion. pairs arrowboth arrowboth arrowboth arrowboth
Answer: After matching each set of conditions with the corresponding relationship between ∆ABC and ∆XYZ and the criterion that proves the relationship the matched pairs are as follows:
1 . AB = XY ,BC = YZ and ∠B ≅ ∠Y ⇒ ΔABC ≅ ΔXYZ by SAS criterion.
2 . AB = XY and ∠A ≅ ∠X and ∠B ≅ ∠Y⇒ ΔABC ≅ ΔXYZ by ASA criterion.
3 . ∠A=∠X,∠B=∠Y and ∠C=∠Z⇒ ΔABC and ΔXYZ are not necessarily congruent.[by AAA similarity criteria both triangles are similar but may not congruent ∵ every congruent triangles have equal sides and equal angles]
4 . AB = XY, BC = YZ and CA = ZX ⇒ ΔABC ≅ ΔXYZ by the SSS criterion.
