Questions and Answers
What is the Orthocenter?
The point of intersection of the three altitudes.
What is the Centroid?
The point of intersection of the three medians.
What is the Circumcenter?
The point of intersection of the three perpendicular bisectors.
What is the Incenter?
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What are medians in a triangle?
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What are perpendicular bisectors?
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What are angle bisectors?
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What are altitudes in a triangle?
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What is a vertex angle in an isosceles triangle?
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What is a Midsegment?
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What does the Perpendicular Bisector Theorem state?
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Study Notes
Orthocenter
- Intersection of the three altitudes of a triangle.
- Altitudes are segments drawn from each vertex perpendicular to the opposite side.
Centroid
- Formed by the intersection of the three medians in a triangle.
- Medians connect each vertex to the midpoint of the opposite side, dividing each median into a 1:2 ratio.
Circumcenter
- Located at the intersection of the three perpendicular bisectors of a triangle's sides.
- In right triangles, it is positioned at the midpoint of the hypotenuse, equidistant from all three vertices.
Incenter
- Intersection point of the angle bisectors within a triangle.
- Always located inside the triangle and equidistant from all three sides.
Medians
- Segments running from a vertex to the midpoint of the opposite side.
- Essential for determining the centroid and balances the triangle's mass.
Perpendicular Bisectors
- Lines that intersect each side of the triangle at its midpoint and are perpendicular to that side.
- Play a crucial role in locating the circumcenter.
Angle Bisectors
- Lines that divide an angle into two equal parts.
- Important for finding the incenter of the triangle.
Altitudes
- Segments drawn from a vertex to the line containing the opposite side, meeting the side at a right angle.
- Useful in finding the orthocenter.
Vertex Angle
- The angle formed between two equal sides in an isosceles triangle.
- Distinguishes the isosceles triangle from other types.
Midsegment
- A segment connecting the midpoints of two sides of a triangle.
- This segment is parallel to the third side and is half its length.
Perpendicular Bisector Theorem
- Any point on a perpendicular bisector is equidistant from the segment's endpoints.
- This property is used to show the circumcenter's equal distance to all triangle vertices.
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Description
Test your knowledge of the key points in a triangle, including the orthocenter, centroid, circumcenter, and incenter. This quiz features flashcards that define each term and explain their significance in triangle geometry.
