Question

Match each set of conditions with the corresponding relationship between ∆abc and ∆xyz and the criterion (if any) that proves the 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 1

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.

Answer 2

The pairs are:

1 ) AB = XY ,BC = YZ and angle B is congruent to angle Y   ↔   
↔  ΔABC and ΔXYZ are congruent by the SAS criterion.

2 )   AB = XY  and angles A and B are congruent to angles X and Y, respectively  ↔  ΔABC and ΔXYZ are congruent by the ASA criterion.

3 )   Angles A, B  and C are congruent to angles  X, Y and Z, respectively.   ↔  ΔABC and ΔXYZ are not necessarily congruent.

4 ) AB = XY, BC = YZ and CA = ZX ↔ ΔABC and ΔXYZ are congruent by the SSS criterion.