Geometry Chapter 5 Review Flashcards

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Questions and Answers

What is the definition of a median?

A line that divides an angle into two equal parts.

A segment from the vertex of the triangle to the opposite side.

A segment whose endpoints are in the vertex of the triangle and the midpoint of the opposite side. (correct)

A segment that connects two midpoints of a triangle.

What is a centroid?

The point of concurrency for the three medians in a triangle.

What does the centroid theorem state?

The top half of the vertical line is $\frac{2}{3}$ of the lower portion of the vertical line.

The centroid is always located inside the triangle.

True Signup and view all the answers

How does the centroid divide the median?

Into two parts with a ratio of 2:1. Signup and view all the answers

What is the definition of an altitude in a triangle?

Perpendicular segments from the vertex of a triangle to the line containing the opposite side. Signup and view all the answers

What is an orthocenter?

The point of concurrency of the three altitudes in a triangle. Signup and view all the answers

What defines a midsegment of a triangle?

A segment joining the midpoints of two sides of a triangle. Signup and view all the answers

The midsegment is half of the lower segment.

True Signup and view all the answers

What is a locus in geometry?

A set of points that satisfies a certain condition. Signup and view all the answers

What does the perpendicular bisector theorem state?

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

What is the converse of the perpendicular bisector theorem?

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

What are concurrent lines?

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

What is a point of concurrency?

The point where concurrent lines intersect. Signup and view all the answers

What is a circumcenter?

The point of concurrency for three perpendicular bisectors. Signup and view all the answers

What does the circumcenter theorem state?

If circumcenter is the circumcenter of a triangle, then it is equidistant from the vertices. Signup and view all the answers

What is a circumscribed circle?

A circle that contains all the vertices of a polygon. Signup and view all the answers

What does the angle bisector theorem state?

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

What is the converse of the angle bisector theorem?

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

What is an incenter?

The point of concurrency for three angle bisectors. Signup and view all the answers

What does the incenter theorem state?

If incenter is the incenter of a triangle, then it is equidistant from the three sides of the triangle. Signup and view all the answers

What is an inscribed circle?

A circle inscribed in a polygon that intersects each side at exactly one point. Signup and view all the answers

What does the exterior angle inequality state?

The measure of the exterior angle is greater than either of its remote interior angles. Signup and view all the answers

What does the triangle inequality theorem state?

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Signup and view all the answers

What does the hinge theorem state?

If two sets of sides are congruent and included angles (hinges) are not congruent, then the larger hinged angle is across from the longer side. Signup and view all the answers

What is the converse of the hinge theorem?

If two sets of sides are congruent and the third sides are not, then the longer side is across from the larger hinged angle. Signup and view all the answers

Study Notes

Median

A median connects a triangle's vertex to the midpoint of the opposite side.

Centroid

The centroid is where the three medians of a triangle intersect.
It acts as the triangle's balancing point and is always located inside the triangle.

Centroid Theorem

The segment created by a median is divided by the centroid into two sections, with the upper section measuring 2/3 of the total median length.

Altitude

An altitude is a perpendicular segment from a triangle's vertex to the line containing the opposite side.

Orthocenter

The point where the three altitudes of a triangle intersect is called the orthocenter.

Midsegment

A midsegment connects the midpoints of two sides of the triangle and is half the length of the base segment it parallels.

Locus

A locus is a collection of points that fulfill a specific condition.

Perpendicular Bisector Theorem

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

Converse of Perpendicular Bisector Theorem

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

Concurrent Lines

Concurrent lines are three or more lines that meet at a single point, known as the point of concurrency.

Circumcenter

The circumcenter is where the three perpendicular bisectors of a triangle intersect.

Circumcenter Theorem

The circumcenter is equidistant from all vertices of the triangle.

Circumscribed Circle

A circumcircle surrounds a polygon, touching all its vertices.

Angle Bisector Theorem

A point on the bisector of an angle remains equidistant from the angle's sides.

Converse of the Angle Bisector Theorem

If a point in the interior of an angle is equidistant from its sides, it must lie on the angle bisector.

Incenter

The incenter is the intersection point of the three angle bisectors of a triangle.

Incenter Theorem

The incenter is equidistant from all three sides of the triangle.

Inscribed Circle

An inscribed circle touches each side of a polygon at exactly one point.

Exterior Angle Inequality

An exterior angle of a triangle is greater than the measures of either of its remote interior angles.

Triangle Inequality Theorem

For any triangle, the sum of lengths of any two sides must exceed the length of the third side.

Hinge Theorem

If two sides are congruent but the included angles are not, the larger angle lies opposite the longer side.

Converse of Hinge Theorem

If two sets of sides are congruent, the longer side is opposite the larger angle.

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Description

Test your knowledge of key concepts in Geometry Chapter 5 with these flashcards. This review covers important terms such as median, centroid, and centroid theorem, helping reinforce your understanding of triangle properties. Perfect for quick studying and revision.