Median, Altitude, Midsegment and Triangle Inequalities

Front

What is the median of a triangle?

Back

A median of a triangle is a line segment joining a vertex to the midpoint of the opposite side.

Front

What is the altitude of a triangle?

Back

An altitude of a triangle is a perpendicular segment from a vertex to the line containing the opposite side.

Front

What is a midsegment in a triangle?

Back

A midsegment is a line segment that connects the midpoints of two sides of a triangle.

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 do you find the length of a median in a triangle?

Back

The length of a median can be found using the formula: m = 1/2 * sqrt(2a^2 + 2b^2 - c^2), where a and b are the lengths of the sides adjacent to the median and c is the length of the opposite side.

Front

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

Back

In a triangle, the larger the angle, the longer the opposite side; conversely, the shorter the angle, the shorter the opposite side.

Front

What does an angle bisector do?

Back

An angle bisector divides an angle into two equal parts.

Front

Can a triangle have sides of lengths 7, 8, and 15?

Back

No, because 7 + 8 is not greater than 15, violating the Triangle Inequality Theorem.

Front

What is the significance of the midsegment in a triangle?

Back

The midsegment of a triangle is parallel to the third side and its length is half the length of that side.

Front

How do you determine the smallest angle in a triangle?

Back

The smallest angle in a triangle is opposite the shortest side.