Midsegments and Medians and more

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. It is parallel to the third side and its length is half the length of that side.

Front

What is the centroid of 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 and divides each median into a ratio of 2:1.

Front

If G is the centroid of triangle ABC and BE= 18, what is the length of BG?

Back

12

Front

If G is the centroid of triangle ABC and GE= 7, what is the length of BE?

Back

21

Front

What does the SSS congruence theorem state?

Back

The SSS (Side-Side-Side) congruence theorem states that if three sides of one triangle are equal to three sides of another triangle, then the two triangles are congruent.

Front

How do you find the length of a midsegment?

Back

To find the length of a midsegment, take the average of the lengths of the two sides it connects and divide by 2.

Front

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

Back

The centroid divides each median into two segments, with the longer segment being twice the length of the shorter segment.

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

If the lengths of two sides of a triangle are 10 and 14, what is the length of the midsegment connecting these two sides?

Back

12 (the midsegment is half the length of the third side, which is 24 in this case).

Front

What is the formula for finding the area of a triangle using the lengths of its medians?

Back

Area = (4/3) * sqrt(s * (s - m1) * (s - m2) * (s - m3)), where s = (m1 + m2 + m3) / 2 and m1, m2, m3 are the lengths of the medians.