Question

Can you prove that the two triangles are similar? Justify your answer.

Answer 1

To prove that 2 triangles are similar we need

either

1) values of tree sides of the both triangles that should be proportional (SSS), either

2)values of 2 corresponding angles that should be congruent (AA),

either

3) values of 2 sides in both triangles (that should be proportional) and angle between them (that are congruent) in both triangles (SAS).

WE do not have any of these data, so we cannot prove that triangles are similar.

Answer 2

Answer: The justified answer is given below.

Step-by-step explanation: We are asked whether we can prove the two triangles shown in the figure are similar. Also, to justify the answer.

From the figure, we note that

The lengths of the two sides of first triangle are 4 units and 5 units. And, the lengths of the corresponding sides of the second triangle are 20 units and 25 units.

So, we get

`(4)/(20)=(5)/(25)=(1)/(5).`

That is, the two pairs of corresponding sides are proportional.

Also, the measure of the angle lying between the two corresponding pairs of proportional sides are equal.

Therefore, by side-angle-side (SAS) similarity postulate, we find that the given two triangles are SIMILAR.