6-3 Entry Ticket - Medians and Altitudes

Front

What is a median in a triangle?

Back

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

Front

What is an altitude in a triangle?

Back

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

Front

If AD is a median in triangle ABC, what can be said about segments AB and AC?

Back

Segments AB and AC are equal in length.

Front

In triangle ABC, if segment AM is a median, what is the relationship between segments BM and MC?

Back

Segments BM and MC are equal in length.

Front

Given AD = 12, find AG if G is the midpoint of segment AD.

Back

AG = 6.

Front

If segment AM is a median and BC = 34, what can be inferred about the lengths of AB and AC?

Back

AB and AC can be any lengths as long as they satisfy the triangle inequality.

Front

Identify whether AD is a median, altitude, neither, or both.

Back

AD is both a median and an altitude.

Front

What is the formula for finding the length of a median in a triangle?

Back

The length of a median can be calculated 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

If the lengths of sides AB and AC are 17 and 27 respectively, what is the maximum possible length of side BC?

Back

The maximum possible length of side BC is 44.

Front

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

Back

The lengths of the medians are always less than the lengths of the sides they bisect.