Questions and Answers
What is the segment that joins the midpoints of two sides of the triangle?
What is a line, segment, ray, or plane that intersects a segment at its midpoint?
What is the length of the perpendicular segment from a point to a line?
Distance from a point to a line
What do you call three or more lines that meet at one point?
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What is a line, segment, or ray that is perpendicular to the triangle at its midpoint?
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What is the point of concurrency for perpendicular bisectors called?
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What do you call a ray that divides the triangle into two congruent triangles?
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What is the point of concurrency for angle bisectors known as?
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What does it mean when a circle is inside the triangle?
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What does it mean when a circle goes around the triangle?
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What is a segment that starts at a vertex and goes to the midpoint of the opposite side called?
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What is the point of concurrency of a median known as?
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What is a perpendicular segment from a vertex to the opposite side forming a right angle called?
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What is the point of concurrency of altitudes referred to as?
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What is defined as having the opposite meaning of the original statement?
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What are statements with the same truth value known as?
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What type of reasoning considers all possibilities and proves all but one false?
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What is it called when a statement and its negation are the only possibilities?
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What is the theorem that states if a segment joins the midpoints of two sides of a triangle, then it is parallel and half as long as the third side?
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What symbols are used for inverse?
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What symbols represent the contrapositive?
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What are the steps for indirect proofs?
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Study Notes
Geometry Terms and Definitions
- Midsegment: A line segment connecting the midpoints of two sides of a triangle.
- Segment Bisector: A geometric entity (line, segment, ray, or plane) that intersects a segment at its midpoint.
- Distance from a Point to a Line: The length of the perpendicular segment from a given point to the line.
- Concurrent: Refers to three or more lines that intersect at a single point.
- Perpendicular Bisector: A line, segment, or ray that is perpendicular to a triangle at the midpoint of a side.
- Circumcenter: The point where the perpendicular bisectors of a triangle meet, indicating the center of the circumcircle.
Triangle Properties
- Angle Bisector: A ray that divides an angle into two congruent angles, hence splitting the triangle into two congruent triangles.
- Incenter: The point of concurrency for the angle bisectors of a triangle, representing the center of the inscribed circle.
- Inscribed Circle: A circle drawn inside the triangle, touching all three sides.
- Circumscribed Circle: A circle that encloses the triangle, touching all three vertices.
Medians and Concurrency
- Median: A segment that starts at a vertex of the triangle and extends to the midpoint of the opposite side.
- Centroid: The point where all three medians of a triangle converge.
- Altitude: A perpendicular segment drawn from a vertex to the opposite side, forming a right angle.
- Orthocenter: The point of concurrency of all three altitudes in a triangle.
Logical Statements and Proofs
- Negation: A statement that has the opposite meaning of the original statement.
- Equivalent Statements: Two statements that hold the same truth value.
- Indirect Reasoning: A method of reasoning where all possibilities are examined and all but one is proven false.
- Indirect Proof: A method of proof involving the declaration that only a statement and its negation exist as possibilities.
Theorems and Symbols
- Triangle Midsegment Theorem: States that if a segment connects the midpoints of two sides of a triangle, it is parallel to the third side and half its length.
- Inverse Symbol: Represented as ~p → ~q, indicating the negation of both the hypothesis and conclusion.
- Contrapositive Symbol: Denoted as ~q → ~p, representing the negation of the conclusion and hypothesis.
- Steps for Indirect Proofs: Include negating the given statement, assuming it leads to a contradiction, and concluding that the assumption must be false while affirming the truth of the proven statement.
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Description
Test your knowledge of key concepts in Geometry Chapter 5. These flashcards cover essential terms such as midsegment, segment bisector, and the distance from a point to a line. Perfect for students preparing for exams or needing a refresher on geometry concepts.
