Geometry Chapter 5 Flashcards

Questions and Answers

What does the Triangle Midsegment Theorem state?

The segment is equal to the third side.

The segment is parallel to the third side. (correct)

The segment is twice as long as the third side.

The segment is perpendicular to the third side.

What is a Midsegment in a triangle?

Segment connecting the midpoints of two sides of a triangle.

What does the term Equidistant mean?

Equal distance away from two objects.

What does the Perpendicular Bisector Theorem imply?

If a point is on the bisector, it is equidistant from the endpoints. Signup and view all the answers

What does the Converse of the Perpendicular Bisector Theorem state?

A point equidistant from the endpoints lies on the perpendicular bisector. Signup and view all the answers

What is the Angle Bisector Theorem?

If a point is on the bisector of an angle, then the point is equidistant from the sides of the angle. Signup and view all the answers

What does the Converse of Angle Bisector Theorem indicate?

Being equidistant from the angle sides means it’s on the bisector. Signup and view all the answers

What does Concurrent mean?

When three or more lines intersect at one point. Signup and view all the answers

What is a Point of Concurrency?

The point at which three or more lines intersect. Signup and view all the answers

What is a Circumcenter?

The point of concurrency of the perpendicular bisectors of a triangle. Signup and view all the answers

What does Circumscribe mean in reference to a triangle?

The circle that is around the triangle touching all points (vertices). Signup and view all the answers

What is an Incenter?

The point of concurrency of the angle bisectors of a triangle. Signup and view all the answers

What does Inscribe mean?

The circle that is inside the triangle. Signup and view all the answers

What is a Median in a triangle?

A segment whose endpoints are a vertex and the midpoint of the opposite side. Signup and view all the answers

What is a Centroid?

The point of concurrency of the medians. Signup and view all the answers

What is an Altitude in a triangle?

The perpendicular segment from a vertex of the triangle to the line containing the opposite side. Signup and view all the answers

What is an Orthocenter?

The point of concurrency of the altitudes. Signup and view all the answers

What is an Angle Bisector?

A ray that divides an angle into two congruent angles. Signup and view all the answers

What is a Perpendicular Bisector?

A line, segment, or ray that is perpendicular to the segment at its midpoint. Signup and view all the answers

Study Notes

Triangle Midsegment Theorem

A segment that connects the midpoints of two sides of a triangle is parallel to the third side.
This segment measures half the length of the third side.

Midsegment

Defined as the segment that joins the midpoints of two sides of a triangle.

Equidistant

Refers to being equal distance from two objects or points.

Perpendicular Bisector Theorem

A point located on the perpendicular bisector of a line segment is equidistant from the segment's endpoints.

Converse of the Perpendicular Bisector Theorem

If a point is equidistant from the endpoints of a segment, then it lies on the perpendicular bisector of that segment.

Angle Bisector Theorem

A point on the bisector of an angle is equidistant from the angle’s sides.

Converse of Angle Bisector Theorem

A point within the interior of an angle that is equidistant from the angle's sides lies on the angle bisector.

Concurrent

Describes a scenario where three or more lines intersect at a single point.

Point of Concurrency

The specific point where three or more lines intersect.

Circumcenter

The point of concurrency formed by the perpendicular bisectors of a triangle.

Circumscribe

Refers to a circle that surrounds a triangle and touches all its vertices.

Incenter

The point of concurrency of the angle bisectors in a triangle.

Inscribe

A circle that is contained within a triangle, touching all sides.

Median

A segment that connects a vertex of a triangle to the midpoint of the opposite side.

Centroid

The point where the medians of a triangle intersect.

Altitude

The perpendicular segment drawn from a vertex of a triangle to the line containing the opposite side.

Orthocenter

The point of concurrency formed by the altitudes of a triangle.

Angle Bisector

A ray that divides an angle into two equal (congruent) angles.

Perpendicular Bisector

A line, segment, or ray that is perpendicular to another segment at its midpoint.

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Description

Test your knowledge of the key terms and concepts from Geometry Chapter 5 with these flashcards. Each card features a term along with its definition, including important theorems related to triangles and segments. Enhance your understanding of geometric principles!