Question

Two angles and one side in a triangle are equivalent to those in another triangle. Are the remaining sides and angles equivalent?

Answer 1

Only if the one side is between the two angles. If not, then we can't say. Maybe the rest are, and maybe they're not.

Answer 2

Answer with explanation:

It is given that Two angles and one side in a triangle are equivalent to those in another triangle.

Let A , B and C are two angles of Triangle.And P, Q and R are three Angles of another Triangle.

A=P-----(a)

B=Q-------(b)

→A+B+C=180°-----[Using Angle sum property of triangle]----(1)

→P+Q+R=180°-----[Using Angle sum property of triangle]----(2)

From (1) and (2)

→A+B+C=P+Q+R

Using a and b

→ C=R

⇒So,third Angle of two triangles are equal to each other .

⇒Now information about other two sides is not given.But the two triangles will be similar by Angle-Angle (Abbreviated as AA) Similarity.

⇒So,if the Triangles are similar then their corresponding sides will be proportional.

So,Third side will be equal to each other and corresponding side will be Proportional to each other.