Big Ideas Math® Geometry Chapter 6 Flashcards

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Questions and Answers

What does equidistant mean?

The same distance apart from each figure.

What is the Perpendicular Bisector Theorem?

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

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.

What does the Angle Bisector Theorem state?

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

What is the Converse of the Angle Bisector Theorem?

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

What does concurrent mean in geometry?

When three or more lines, rays, or segments intersect at the same point. Signup and view all the answers

What is the point of concurrency?

The point of intersection of concurrent lines, rays, or segments. Signup and view all the answers

What is the circumcenter of a triangle?

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

What does the Circumcenter Theorem state?

The circumcenter of a triangle is equidistant from the vertices of the triangle. Signup and view all the answers

What is the Incenter?

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

What does the Incenter Theorem state?

The incenter of a triangle is equidistant from the sides of the triangle. Signup and view all the answers

What is a median of a triangle?

A segment from a vertex to the midpoint of the opposite side. Signup and view all the answers

What is the centroid of a triangle?

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

What does the Centroid Theorem state?

The centroid is located 2/3 of the distance from each vertex to the midpoint of the opposite side. Signup and view all the answers

What is the altitude of a triangle?

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

What is the orthocenter of a triangle?

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

What is a midsegment of a triangle?

A line segment that connects the midpoints of two sides of a triangle. Signup and view all the answers

What does the Triangle Midsegment Theorem state?

A midsegment connecting two sides of a triangle is parallel to the third side and is half as long. Signup and view all the answers

What is an indirect proof?

A proof in which the statement to be proved is assumed to be false and a contradiction is shown. Signup and view all the answers

What does the Triangle Longer Side Theorem state?

If one side of a triangle is longer than another side, then the angle opposite the longer side is larger than the angle opposite the shorter side. Signup and view all the answers

What does the Triangle Larger Angle Theorem state?

If one angle of a triangle is larger than another angle, then the side opposite the larger angle is longer than the side opposite the smaller angle. 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 is greater than the length of the third side. Signup and view all the answers

What does the Hinge Theorem state?

If two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first is larger than the included angle of the second, then the third side of the first is longer than the third side of the second. Signup and view all the answers

What is the Converse of the Hinge Theorem?

If two sides of one triangle are congruent to two sides of another triangle, and the third side of the first is longer than the third side of the second, then the included angle of the first is larger than the included angle of the second. Signup and view all the answers

Study Notes

Geometry Key Concepts

Equidistant: Figures or points that are the same distance apart from each other.
Perpendicular Bisector Theorem: A point located on the perpendicular bisector of a segment is equidistant from the segment's endpoints.
Converse of the Perpendicular Bisector Theorem: A point that is equidistant from the endpoints of a segment must lie on the segment's perpendicular bisector.
Angle Bisector Theorem: A point located on the bisector of an angle is equidistant from the two sides of that angle.
Converse of the Angle Bisector Theorem: A point that is equidistant from the sides of an angle lies on that angle's bisector.
Concurrent: Describes when three or more lines, rays, or segments intersect at a single point.
Point of Concurrency: The specific point where concurrent lines, rays, or segments meet.
Circumcenter of a Triangle: The point where the perpendicular bisectors of a triangle intersect, also equidistant from all triangle vertices.
Circumcenter Theorem: The circumcenter is equidistant from all vertices of a triangle.
Incenter: The point where the angle bisectors of a triangle intersect, also equidistant from all triangle sides.
Incenter Theorem: The incenter is equidistant from all sides of the triangle it belongs to.
Median of a Triangle: A line segment connecting a vertex of the triangle to the midpoint of the opposite side.
Centroid of a Triangle: The intersection point of a triangle’s medians.
Centroid Theorem: The centroid divides each median into two segments in a 2:1 ratio, with the longer segment being closer to the vertex.
Altitude of a Triangle: A perpendicular line segment drawn from a vertex to the opposite side or its extension.
Orthocenter of a Triangle: The intersection point of the three altitudes of a triangle.
Midsegment of a Triangle: A segment connecting the midpoints of two sides of a triangle.
Triangle Midsegment Theorem: A midsegment of a triangle is parallel to the third side and its length is half that of the third side.
Indirect Proof: A method of proving a statement by assuming it is false and demonstrating a contradiction.
Triangle Longer Side Theorem: If one side of a triangle is longer than another, the angle opposite the longer side is larger than the angle opposite the shorter side.
Triangle Larger Angle Theorem: If one angle of a triangle is greater than another, the side opposite the larger angle is longer than the side opposite the smaller angle.
Triangle Inequality Theorem: States that the sum of any two sides of a triangle is greater than the length of the third side.
Hinge Theorem: If two sides of one triangle are congruent to two sides of another triangle, and the angle between the first triangle's sides is larger than the angle between the second triangle's sides, then the third side of the first triangle is longer.
Converse of the Hinge Theorem: If two sides of one triangle and the third side of another are compared, and the first side is longer, the included angle of the first triangle is larger than that of the second.

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Explore key concepts from Geometry Chapter 6 with these flashcards. Test your understanding of terms such as 'equidistant' and the 'Perpendicular Bisector Theorem'. Perfect for reinforcing your knowledge in geometry.