Suppose right triangle ABC has one acute angle 47º. Suppose also that right triangle DEF has an acute angle 43º. How are triangles ABC and DEF related?
A right triangle with an acute angle of 47 degrees must have a second acute angle of 43 degrees. Therefore the two triangles are similar. They both have the same angles of 90, 47 and 43 degrees.
Suppose right triangle ABC has one acute angle 47º. Suppose also that right triangle DEF has an acute angle 43º. How are triangles ABC and DEF related?
To determine how triangles ABC and DEF are related, we can compare their corresponding angles.
In triangle ABC, one of the acute angles is 47º. Since the sum of the angles in a triangle is always 180º, the other acute angle in triangle ABC can be found by subtracting 90º (the right angle) and 47º from 180º:
180º - 90º - 47º = 43º
Triangle ABC has one acute angle measuring 43º, which is the same as the acute angle in triangle DEF. This means that the two triangles have one pair of congruent (equal) angles. By the Angle-Angle (AA) criterion, if two triangles have two pairs of corresponding congruent angles, they are similar.
Therefore, triangles ABC and DEF are similar because they have one pair of congruent angles.