Ordering Sides and Angles in Triangles

Front

What is the relationship between the angles and sides in a triangle?

Back

In a triangle, the larger the angle, the longer the opposite side. Conversely, the smaller the angle, the shorter the opposite side.

Front

How do you order angles in a triangle from smallest to largest?

Back

To order angles in a triangle from smallest to largest, compare their measures. The angle with the smallest measure is first, followed by the next smallest, and so on.

Front

What is the Triangle Inequality Theorem?

Back

The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Front

How can you determine the longest side of a triangle?

Back

The longest side of a triangle is opposite the largest angle. To find it, first identify the largest angle.

Front

What is the significance of the angles in triangle classification?

Back

Triangles can be classified based on their angles as acute (all angles < 90°), right (one angle = 90°), or obtuse (one angle > 90°).

Front

What is the significance of the sides in triangle classification?

Back

Triangles can be classified based on their sides as equilateral (all sides equal), isosceles (two sides equal), or scalene (all sides different).

Front

How do you find the measure of an unknown angle in a triangle?

Back

To find an unknown angle in a triangle, use the fact that the sum of all angles in a triangle is 180°. Subtract the sum of the known angles from 180°.

Front

What is the relationship between the sides of a triangle and its angles?

Back

In a triangle, the side lengths are proportional to the sine of their opposite angles, as described by the Law of Sines.

Front

What is the Law of Sines?

Back

The Law of Sines states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant for all three sides and angles.

Front

What is the Law of Cosines?

Back

The Law of Cosines relates the lengths of the sides of a triangle to the cosine of one of its angles: c² = a² + b² - 2ab*cos(C).