UNIT 6: Relationships within Triangles

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.

Front

What is a midsegment in a triangle?

Back

A midsegment is a 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

How do you find the length of a midsegment in a triangle?

Back

To find the length of a midsegment, measure the lengths of the two sides it connects, and use the formula: Length of midsegment = (1/2) * (length of the third side).

Front

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

Back

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

Front

How do you order the sides of a triangle from shortest to longest?

Back

To order the sides, compare the angles opposite each side. The side opposite the smallest angle is the shortest, and the side opposite the largest angle is the longest.

Front

What is the formula for finding the area of a triangle?

Back

The area of a triangle can be found using the formula: Area = (1/2) * base * height.

Front

What is the significance of the centroid in a triangle?

Back

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

Front

How do you determine the length of a segment in a triangle using the centroid?

Back

If a point is the centroid, it divides each median into a ratio of 2:1, with the longer part being closer to the vertex.

Front

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

Back

The larger the angle, the longer the side opposite it. This is known as the triangle inequality theorem.

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.