Geometry: 8.2 Angle Bisectors of Triangles

Front

What is an angle bisector?

Back

An angle bisector is a line or segment that divides an angle into two equal parts.

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 relationship between the sides and angles of a triangle?

Back

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

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

Can the lengths 2, 15, and 16 form a triangle?

Back

Yes, because 2 + 15 > 16, 2 + 16 > 15, and 15 + 16 > 2.

Front

Can the lengths 4, 7, and 8 form a triangle?

Back

Yes, because 4 + 7 > 8, 4 + 8 > 7, and 7 + 8 > 4.

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

What is the significance of the centroid in a triangle?

Back

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

Front

What is a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees.

Front

What is the Pythagorean theorem?

Back

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.