Savvas - Topic 5 Relationships in Triangles

Front

What is the Triangle Inequality Theorem?

Back

The Triangle Inequality Theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Front

If the lengths of two sides of a triangle are 2 and 6, what is the range of possible values for the third side?

Back

Front

What is a circumcenter?

Back

The circumcenter is the point where the perpendicular bisectors of the sides of a triangle intersect. It is equidistant from all three vertices of the triangle.

Front

How do you find the length of a side in a triangle using the circumcenter?

Back

To find the length of a side using the circumcenter, you can use the property that the distance from the circumcenter to each vertex is equal to the circumradius.

Front

What is the incenter of a triangle?

Back

The incenter is the point where the angle bisectors of a triangle intersect. It is equidistant from all three sides of the triangle.

Front

If the inradius of a triangle is 8, what does this mean?

Back

An inradius of 8 means that the distance from the incenter to each side of the triangle is 8 units.

Front

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

Back

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

Front

What is the formula for the area of a triangle given its base and height?

Back

Front

How do you determine if three lengths can form a triangle?

Back

To determine if three lengths can form a triangle, check if they satisfy the Triangle Inequality Theorem: the sum of the lengths of any two sides must be greater than the length of the third 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. It is the center of mass and divides each median into a 2:1 ratio.