Median & Altitude HW

Front

What is the definition of a centroid in a triangle?

Back

The centroid is the point where the three medians of a triangle intersect. It is also the center of mass of the triangle.

Front

In triangle ABC, if AG = 3x + 15 and BG = 5x + 9, how do you find the value of x?

Back

Set AG = BG since G is the centroid. Therefore, 3x + 15 = 5x + 9. Solving gives x = 3.

Front

What is a median in a triangle?

Back

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

Front

What is the relationship between the lengths of the segments created by the centroid on the medians?

Back

The centroid divides each median into two segments, with the segment connecting the vertex to the centroid being twice as long as the segment connecting the centroid to the midpoint.

Front

Back

Front

What is the definition of an altitude in a triangle?

Back

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

Front

In triangle ABC, if AC is an altitude, what can be said about angle ACB?

Back

Angle ACB is a right angle (90 degrees) because the altitude creates a right triangle.

Front

How do you find the length of a median using the lengths of the sides of the triangle?

Back

Front

What is the difference between a median and an angle bisector?

Back

A median connects a vertex to the midpoint of the opposite side, while an angle bisector divides an angle into two equal parts.

Front

If the lengths of sides AB and AC are 5 and 12 respectively, what is the length of the median to side BC?

Back