If in two right triangles, one of the acute angles of one triangle is equal to an acute angle of the other triangle, can you say that the two triangles will be similar? Why?
Answer:
Yes.
Video Explanation:
Detailed Answer with Explanation:
Let us go step by step:
In both triangles, one angle is a right angle (90°).
It is given that one acute angle of the first triangle is equal to one acute angle of the second triangle.
A triangle has three angles. The sum of all three angles of any triangle is 180°.
So, in each triangle we already know two angles: one is 90° (right angle), and the other is the given equal acute angle.
That means the third angle in both triangles must also be equal (because 180° − (90° + given angle) will give the same result for both).
Therefore, the two triangles have all their angles equal.
By the Angle–Angle (AA) similarity rule, if two angles of one triangle are equal to two angles of another triangle, the triangles are similar.