Podcast
Questions and Answers
What is the definition of a median?
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?
What is a centroid?
The point of concurrency for the three medians in a triangle.
What does the centroid theorem state?
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.
The centroid is always located inside the triangle.
How does the centroid divide the median?
How does the centroid divide the median?
What is the definition of an altitude in a triangle?
What is the definition of an altitude in a triangle?
What is an orthocenter?
What is an orthocenter?
What defines a midsegment of a triangle?
What defines a midsegment of a triangle?
The midsegment is half of the lower segment.
The midsegment is half of the lower segment.
What is a locus in geometry?
What is a locus in geometry?
What does the perpendicular bisector theorem state?
What does the perpendicular bisector theorem state?
What is the converse of the perpendicular bisector theorem?
What is the converse of the perpendicular bisector theorem?
What are concurrent lines?
What are concurrent lines?
What is a point of concurrency?
What is a point of concurrency?
What is a circumcenter?
What is a circumcenter?
What does the circumcenter theorem state?
What does the circumcenter theorem state?
What is a circumscribed circle?
What is a circumscribed circle?
What does the angle bisector theorem state?
What does the angle bisector theorem state?
What is the converse of the angle bisector theorem?
What is the converse of the angle bisector theorem?
What is an incenter?
What is an incenter?
What does the incenter theorem state?
What does the incenter theorem state?
What is an inscribed circle?
What is an inscribed circle?
What does the exterior angle inequality state?
What does the exterior angle inequality state?
What does the triangle inequality theorem state?
What does the triangle inequality theorem state?
What does the hinge theorem state?
What does the hinge theorem state?
What is the converse of the hinge theorem?
What is the converse of the hinge theorem?
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.
Studying That Suits You
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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.
