Geometry Chapter 5 Test Flashcards

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Questions and Answers

What is the segment that joins the midpoints of two sides of the triangle?

Altitude

Midsegment (correct)

Bisector

Median

What is a line, segment, ray, or plane that intersects a segment at its midpoint?

Midsegment

Segment bisector (correct)

Angle bisector

Altitude

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?

Concurrent Signup and view all the answers

What is a line, segment, or ray that is perpendicular to the triangle at its midpoint?

Perpendicular bisector Signup and view all the answers

What is the point of concurrency for perpendicular bisectors called?

Circumcenter Signup and view all the answers

What do you call a ray that divides the triangle into two congruent triangles?

Angle bisector Signup and view all the answers

What is the point of concurrency for angle bisectors known as?

Incenter Signup and view all the answers

What does it mean when a circle is inside the triangle?

Inscribed Signup and view all the answers

What does it mean when a circle goes around the triangle?

Circumscribed Signup and view all the answers

What is a segment that starts at a vertex and goes to the midpoint of the opposite side called?

Median Signup and view all the answers

What is the point of concurrency of a median known as?

Centroid Signup and view all the answers

What is a perpendicular segment from a vertex to the opposite side forming a right angle called?

Altitude Signup and view all the answers

What is the point of concurrency of altitudes referred to as?

Orthocenter Signup and view all the answers

What is defined as having the opposite meaning of the original statement?

Negation Signup and view all the answers

What are statements with the same truth value known as?

Equivalent statements Signup and view all the answers

What type of reasoning considers all possibilities and proves all but one false?

Indirect reasoning Signup and view all the answers

What is it called when a statement and its negation are the only possibilities?

Indirect proof Signup and view all the answers

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?

Triangle midsegment theorem Signup and view all the answers

What symbols are used for inverse?

~p-~q Signup and view all the answers

What symbols represent the contrapositive?

~q-~p Signup and view all the answers

What are the steps for indirect proofs?

Negate the given, show that it is assumed and leads to a contradiction, conclude that the assumption is false and that the prove statement is true. Signup and view all the answers

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.