Midsegment and Perpendicular Bisectors

Front

What is a midsegment in a triangle?

Back

A midsegment is a line segment that connects the midpoints of two sides of a triangle. It is parallel to the third side and its length is half the length of that side.

Front

What is the property of perpendicular bisectors in a triangle?

Back

The perpendicular bisector of a side of a triangle is a line that is perpendicular to that side and divides it into two equal segments. It also passes through the circumcenter of the triangle.

Front

How do you find the circumcenter of a triangle?

Back

To find the circumcenter, construct the perpendicular bisectors of at least two sides of the triangle. The point where they intersect is the circumcenter.

Front

If MP || DE, what can be inferred about the angles formed?

Back

If two lines are parallel, then the corresponding angles formed with a transversal are equal.

Front

What is the relationship between the lengths of the midsegment and the side it is parallel to?

Back

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

Front

Define the term 'congruent segments'.

Back

Congruent segments are segments that have the same length.

Front

What does it mean for two triangles to be congruent?

Back

Two triangles are congruent if their corresponding sides and angles are equal.

Front

How can you determine if two triangles are similar?

Back

Two triangles are similar if their corresponding angles are equal and their corresponding sides are in proportion.

Front

What is the significance of the circumcenter in a triangle?

Back

The circumcenter is the point where the perpendicular bisectors of the sides intersect, and it is equidistant from all three vertices of the triangle.

Front

If a triangle has sides of lengths 6, 8, and 10, what type of triangle is it?

Back

It is a right triangle, as it satisfies the Pythagorean theorem: 6^2 + 8^2 = 10^2.