Perpendicular Bisectors and Midsegments of a Triangle

Front

What is a perpendicular bisector?

Back

A perpendicular bisector is a line that divides a segment into two equal parts at a 90-degree angle.

Front

What is a midsegment of a triangle?

Back

A midsegment of a triangle is a segment that connects the midpoints of two sides of the triangle.

Front

What is the relationship between the lengths of the midsegment and the sides of the triangle?

Back

The length of the midsegment is half the length of the side it is parallel to.

Front

How do you find the midpoint of a segment?

Back

The midpoint can be found by averaging the x-coordinates and the y-coordinates of the endpoints.

Front

If GH = 16 and CH = 12, what is the total length of segment GCH?

Back

The total length of segment GCH is 28.

Front

What does it mean for segments to be parallel?

Back

Parallel segments are lines or segments that run in the same direction and never intersect.

Front

How can you determine if two segments are parallel using slopes?

Back

Two segments are parallel if they have the same slope.

Front

What is the formula for finding the length of a segment between two points (x1, y1) and (x2, y2)?

Back

The length is given by the formula: √((x2 - x1)² + (y2 - y1)²).

Front

If a triangle has sides of lengths 6, 8, and 10, what is the length of the midsegment connecting the sides of lengths 6 and 8?

Back

The length of the midsegment is 4.

Front

What is the significance of the centroid in relation to the medians of a triangle?

Back

The centroid is the point where the three medians of a triangle intersect, and it divides each median into a 2:1 ratio.