HGeom - 5.1-5.4 Review

Front

What is the circumcenter of a triangle?

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 Pythagorean theorem?

Back

For a right triangle, if a and b are the lengths of the legs and c is the length of the hypotenuse, then a² + b² = c².

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

How do you find the coordinates of the orthocenter of a triangle?

Back

The orthocenter is found by determining the intersection of the altitudes of the triangle.

Front

What is the centroid of a triangle?

Back

The centroid is the point where the three medians of a triangle intersect. It is the average of the vertices' coordinates.

Front

Define the term 'concurrency' in geometry.

Back

Concurrency refers to the property of three or more lines intersecting at a single point.

Front

What is the relationship between the circumradius and the area of a triangle?

Back

The circumradius (R) can be calculated using the formula: R = (abc)/(4A), where a, b, and c are the lengths of the sides and A is the area of the triangle.

Front

How do you determine the area of a triangle given its vertices?

Back

The area can be calculated using the formula: Area = 1/2 | x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2) |.

Front

What is the significance of the centroid in a triangle?

Back

The centroid divides each median into a ratio of 2:1, with the longer segment being closer to the vertex.

Front

What is the formula for the circumradius of a triangle?

Back

R = (abc)/(4A), where a, b, c are the lengths of the sides and A is the area.