Question

Triangle QRS has been translated to create triangle Q'R'S'. RS = R'S' = 2 units, angles S and S' are both 28 degrees, and angles R and R' are both 32 degrees. Which postulate below would prove the two triangles are congruent?

a. SSS
b. SAS
c. ASA
d. AAS

Answer 1

You’re given that two angles and a side are congruent, and that the congruent sides are between the two congruent angle pairs. This is an ASA situation, so c.

Answer 2

c. ASA.

Explanation:

Given triangle QRS has been translated to create triangle Q'R'S'.

We are given that

RS=RS'=2 units

Angle S= Angle S'=
`28^(\circ)`

`\angle R=\angle R'= 32^(\circ)`

ASA congruent property: When two triangles are congruent by ASA postulates it means Angle-Side-Angle .

We can say that if two angles and base side of two angles are equal to its corresponding angles and base then triangles are congruent by ASA.

We are given that two angles R and S are equal to its corresponding angles R' and S' and base side RS of two angles R and S equal to its corresponding base side R'S' of two angles R' and S'.

`\therefore`

`\triangle QRS\cong \triangle Q'R'S'`

By ASA ( Angle-Side-Angle ) postulate.

Hence, option c is correct.