Podcast
Questions and Answers
What does 'congruent' mean?
What is a midpoint?
The point in the middle of a segment that bisects the segment.
What are parallel lines?
Two lines that are on the same plane and do not intersect.
What are perpendicular lines?
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What defines an isosceles triangle?
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What are supplementary angles?
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What are complementary angles?
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What is a linear pair?
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What is an angle bisector?
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What is an altitude in a triangle?
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What is a perpendicular bisector?
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What is a median in a triangle?
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What does the Ruler Postulate state?
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What does the Segment Addition Postulate explain?
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What is the Protractor Postulate?
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What is the Angle Addition Postulate?
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What does the Addition Property state?
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What does the Subtraction Property indicate?
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What is the Multiplication Property?
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What does the Division Property state?
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What is the Substitution Property?
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What does the Reflexive Property express?
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What is the Symmetric Property?
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What does the Transitive Property state?
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What is the Distributive Property?
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What is Postulate 5?
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What is Postulate 6?
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What is Postulate 7?
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What is Postulate 8?
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What is Postulate 9?
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What does the SSS Postulate state?
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What does the SAS Postulate indicate?
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What does the ASA Postulate state?
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What does Theorem 1-1 state?
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What does Theorem 1-2 indicate?
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What does Theorem 1-3 state?
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Study Notes
Key Geometry Terms and Definitions
- Congruent: Figures or shapes that are identical in size and shape.
- Midpoint: The specific point that divides a segment into two equal parts, resulting in two congruent segments.
- Parallel Lines: Lines that remain equidistant and never intersect, existing on the same plane.
- Perpendicular Lines: Lines that cross each other at an exact right angle (90 degrees).
Triangle Properties
- Isosceles Triangle: A triangle that has at least two sides of equal length, creating two congruent angles.
- Altitude: A line segment from a vertex to the opposite side, forming a right angle with that side; represents the triangle's height.
- Median: A line segment that connects a vertex of the triangle to the midpoint of the opposite side.
Angle Relationships
- Supplementary Angles: Two angles whose measures add up to 180 degrees.
- Complementary Angles: Two angles that combine to equal 90 degrees.
- Linear Pair: A pair of adjacent angles formed when two lines intersect, yielding a straight line.
Angle Bisector
- Angle Bisector: A ray that divides an angle into two equal parts, creating two congruent angles.
Line Properties
- Perpendicular Bisector: A line that divides a side of a triangle into two equal segments at a right angle.
- Protractor Postulate: Every angle can be measured in degrees using a protractor, similar to how points are measured on a number line.
Postulates and Properties
- Ruler Postulate: Establishes that each point on a line corresponds uniquely to a number.
- Segment Addition Postulate: The sum of two segments along a line equals the larger segment formed.
- Angle Addition Postulate: The sum of two angles equal a larger angle.
Algebraic Properties
- Addition Property: If two quantities are equal, adding the same value to both maintains equality.
- Subtraction Property: Similar to addition, subtracting the same value from both sides keeps equality intact.
- Multiplication Property: Multiplying both sides of an equation by the same value preserves equality.
- Division Property: Dividing both sides by the same non-zero number keeps the equation balanced.
- Substitution Property: An expression can be replaced with an equal expression in any equation.
Logical Properties
- Reflexive Property: Any quantity is equal to itself.
- Symmetric Property: If one quantity equals another, the converse is also true.
- Transitive Property: If one quantity equals a second, and that second equals a third, then the first equals the third.
Geometric Postulates about Points and Lines
- Postulate 5: At least two points are required to form a line; at least three non-collinear points form a plane.
- Postulate 6: Exactly one line can be drawn through any two points.
- Postulate 7: At least one plane exists through any three points, with exactly one plane possible for three non-collinear points.
- Postulate 8 & 9: The intersection of two planes results in a line.
Triangle Congruence Postulates
- SSS Postulate: Triangles are congruent if all three sides of one triangle are equal to those of another.
- SAS Postulate: If two sides and the included angle of one triangle are congruent to the corresponding parts of another, the triangles are congruent.
- ASA Postulate: Two angles and the included side are sufficient to prove triangle congruence.
Intersection Theorems
- Theorem 1-1: Two intersecting lines will intersect at a single point.
- Theorem 1-2: There is one unique plane that contains a line and a point not on that line.
- Theorem 1-3: Two intersecting lines lie in exactly one plane.
Studying That Suits You
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Description
Test your knowledge of geometry theorems with these flashcards. Each card features a key term along with its definition, helping you understand important concepts such as congruence, midpoints, and line relationships. Perfect for students and geometry enthusiasts alike!