Inequalities Within a Triangle

Front

What is an inequality in the context of triangles?

Back

An inequality in triangles refers to the relationship between the lengths of the sides and the measures of the angles, where the longest side is opposite the largest angle, and the shortest side is opposite the smallest angle.

Front

State the Triangle Inequality Theorem.

Back

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

Front

How do you find the midpoint of a line segment?

Back

To find the midpoint of a line segment with endpoints (x1, y1) and (x2, y2), use the formula: Midpoint = ((x1 + x2)/2, (y1 + y2)/2).

Front

If two angles of a triangle are known, how can you find the third angle?

Back

The third angle can be found using the fact that the sum of the angles in a triangle is always 180 degrees. If angles A and B are known, then angle C = 180 - (A + B).

Front

What does it mean for a triangle to be scalene?

Back

A scalene triangle is a triangle in which all three sides are of different lengths and all three angles are of different measures.

Front

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

Back

In a triangle, the largest angle is opposite the longest side, and the smallest angle is opposite the shortest side.

Front

How can you determine which side of a triangle is the longest?

Back

To determine the longest side of a triangle, compare the lengths of the sides or use the angles; the side opposite the largest angle is the longest.

Front

What is the significance of the midpoint in geometry?

Back

The midpoint is significant as it divides a line segment into two equal parts and is often used in various geometric constructions and proofs.

Front

How do you translate a triangle in a coordinate plane?

Back

To translate a triangle in a coordinate plane, add or subtract the same values to the x-coordinates and y-coordinates of each vertex.

Front

What is an acute triangle?

Back

An acute triangle is a triangle where all three angles are less than 90 degrees.