Question

Explain why two right triangles, each with an acute angle of 17°, must be similar.

Answer 1

Two right angles with an acute angle of 17 degrees must be similar because triangles that are similar share the same angles

Answer 2

Explanation:

We can show that the two triangles are similar using the Angle-Angle similarity criterion.

By Angle-Angle similarity criterion, when two angles of one triangle are equal to the two angles of the other triangle, then the two triangles are said to be similar.

Here, it is given that each triangle has an acute angle of 17°.

So, we have one pair of equal angles in the two triangles.

Also, the two triangles are right-angled triangles.

So, each of them will have an angle of 90°.

Since two angles of one triangle are equal to the two angles on the other triangle, the two triangles are similar.