Match each set of conditions with the corresponding relationship between ABC AND XYZ and the criterion(if any) that proves the relationship.

Question

asked Mar 17, 2017 208k views

2 Answers

ChrisPadgham · Answer 1 · 2017-03-22T16:59:22+0000

Answer:

The required pairs are (a)-2, (b)-4, (c)-3, (d)-1.

Explanation:

(a)

According to the SSS postulate two triangles are congruent if all corresponding sides are equal.

In pair 2,

AB=XY,BC=YZ,CA=ZX

So, ΔABC and ΔXYZ are congruent by SSS. For this parts the correct match is pair 2.

(b)

According to the SAS postulate two triangles are congruent if two corresponding sides and their including angle are equal.

In pair 4,

$AB=XY,BC=YZ,\angle B=\angle Y$

So, ΔABC and ΔXYZ are congruent by SAS. For this parts the correct match is pair 4.

(c)

According to the ASA postulate two triangles are congruent if two corresponding angles and their including side are equal.

In pair 3,

$AB=XY,\angle A=\angle X,\angle B=\angle Y$

So, ΔABC and ΔXYZ are congruent by ASA. For this parts the correct match is pair 3.

(d)

In pair 1,

$\angle A=\angle X,\angle B=\angle Y,\angle C=\angle Z$

All corresponding angles are equal. It means ΔABC and ΔXYZ are similar.

It is not necessary that ΔABC and ΔXYZ are congruent.

For this parts the correct match is pair 1.