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: 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.

bhoopendrasisodiya34 bhoopendrasisodiya34 · Answer 2 · 2022-02-01T12:00:30+01:00

Two triangle are congruent when the shape and size of both the triangle are same.The correct set is,

a) ____________3)

b) ____________4)

c) ____________2)

d) ____________1)

What is triangle congruence theorem?

Two triangle are congruent when the shape and size of both the triangle are same.

Triangle congruence theorem are-

Angle-Side-Angle theorem (AAS)- This theorem states that two triangle is congruent when two angle and one side of the triangle are respectively equal to the two angles and same side of the other triangle.

Side-Side-Side theorem (SSS)- When the three sides of the one triangle is equal to the three sides of the other triangle respectively, then the triangle are congruent.

Side-Angle-Side theorem (SAS)- Two sides and the included angle of are equal to the two sides and one angle of other triangle respectively.

Given set is

a) ab = xy, bc = yz, and angle b is congruent to angle y.

1) ∆abc and ∆xyz are congruent by the sss criterion.

b) ab = xy, and angles a and b are congruent to angles x and y, respectively.

2)∆abc and ∆xyz are not necessarily congruent.

c)angles a, b, and c are congruent to angles x, y, and z, respectively.

3)∆abc and ∆xyz are congruent by the sas criterion.

d) ab = xy, bc = yz, and ca = zx.

4)∆abc and ∆xyz are congruent by the asa criterion.

By the triangle congruence theorem, the correct set can be set as shown in the attached image.

Hence the correct set is,

a) ____________3)

b) ____________4)

c) ____________2)

d) ____________1)

Learn more about the congruent triangle here;

https://brainly.com/question/19258025