Special Segments of a Triangle

Front

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

Back

The centroid (G) can be found using the formula: G = ((x1 + x2 + x3)/3, (y1 + y2 + y3)/3).

Front

What is a median in a triangle?

Back

A median of a triangle is a line segment joining a vertex to the midpoint of the opposite side.

Front

How do you find the length of a segment from the centroid to a vertex in a triangle?

Back

The length from the centroid (G) to a vertex (A) is 2/3 of the length of the median from that vertex to the midpoint of the opposite side.

Front

What is the incenter of a triangle?

Back

The incenter is the point where the angle bisectors of a triangle intersect, and it is also the center of the inscribed circle.

Front

How do you find the inradius of a triangle?

Back

The inradius (r) can be found using the formula: r = A/s, where A is the area of the triangle and s is the semi-perimeter.

Front

What is the relationship between the centroid and the medians of a triangle?

Back

The centroid divides each median into two segments, with the segment connecting the centroid to the vertex being twice as long as the segment connecting the centroid to the midpoint of the opposite side.

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, and it is the center of the circumscribed circle.

Front

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

Back

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

Front

What is the significance of parallel segments in triangles?

Back

Parallel segments in triangles can indicate similar triangles and help in solving for unknown lengths using proportionality.

Front

How do you find the length of a segment in a triangle using the properties of similar triangles?

Back

If two triangles are similar, the ratios of corresponding sides are equal, allowing you to set up proportions to find unknown lengths.