7.1 - 7.3 Review - Geometry

Front

What is the formula to find the coordinates of the centroid of a triangle given its vertices (x1, y1), (x2, y2), (x3, y3)?

Back

The coordinates of the centroid (G) are given by G(x, y) = ((x1 + x2 + x3)/3, (y1 + y2 + y3)/3).

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

If the lengths of two segments are in a ratio of 3:4, and the longer segment is 24, what is the length of the shorter segment?

Back

The length of the shorter segment is 18.

Front

What is the relationship between the lengths of segments in a triangle?

Back

In a triangle, the sum of the lengths of any two sides must be greater than the length of the third side (Triangle Inequality Theorem).

Front

If AB = 3x - 8 and DE = 4x + 10, how do you find the value of x when AB = DE?

Back

Set 3x - 8 = 4x + 10 and solve for x.

Front

What is a midpoint in geometry?

Back

A midpoint is a point that divides a line segment into two equal parts.

Front

How do you find the length of a segment if you know the coordinates of its endpoints (x1, y1) and (x2, y2)?

Back

Use the distance formula: Length = √((x2 - x1)² + (y2 - y1)²).

Front

What is the definition of a bisector in geometry?

Back

A bisector is a line, ray, or segment that divides another segment or angle into two equal parts.

Front

If CB = 20, what is the length of DA if they are equal segments?

Back

DA = 20.

Front

What is the difference between a median and a centroid in a triangle?

Back

A median is a line segment from a vertex to the midpoint of the opposite side, while the centroid is the point where all three medians intersect.