Podcast
Questions and Answers
What does 'congruent' mean?
What does 'congruent' mean?
What is a midpoint?
What is a midpoint?
The point in the middle of a segment that bisects the segment.
What are parallel lines?
What are parallel lines?
Two lines that are on the same plane and do not intersect.
What are perpendicular lines?
What are perpendicular lines?
Signup and view all the answers
What defines an isosceles triangle?
What defines an isosceles triangle?
Signup and view all the answers
What are supplementary angles?
What are supplementary angles?
Signup and view all the answers
What are complementary angles?
What are complementary angles?
Signup and view all the answers
What is a linear pair?
What is a linear pair?
Signup and view all the answers
What is an angle bisector?
What is an angle bisector?
Signup and view all the answers
What is an altitude in a triangle?
What is an altitude in a triangle?
Signup and view all the answers
What is a perpendicular bisector?
What is a perpendicular bisector?
Signup and view all the answers
What is a median in a triangle?
What is a median in a triangle?
Signup and view all the answers
What does the Ruler Postulate state?
What does the Ruler Postulate state?
Signup and view all the answers
What does the Segment Addition Postulate explain?
What does the Segment Addition Postulate explain?
Signup and view all the answers
What is the Protractor Postulate?
What is the Protractor Postulate?
Signup and view all the answers
What is the Angle Addition Postulate?
What is the Angle Addition Postulate?
Signup and view all the answers
What does the Addition Property state?
What does the Addition Property state?
Signup and view all the answers
What does the Subtraction Property indicate?
What does the Subtraction Property indicate?
Signup and view all the answers
What is the Multiplication Property?
What is the Multiplication Property?
Signup and view all the answers
What does the Division Property state?
What does the Division Property state?
Signup and view all the answers
What is the Substitution Property?
What is the Substitution Property?
Signup and view all the answers
What does the Reflexive Property express?
What does the Reflexive Property express?
Signup and view all the answers
What is the Symmetric Property?
What is the Symmetric Property?
Signup and view all the answers
What does the Transitive Property state?
What does the Transitive Property state?
Signup and view all the answers
What is the Distributive Property?
What is the Distributive Property?
Signup and view all the answers
What is Postulate 5?
What is Postulate 5?
Signup and view all the answers
What is Postulate 6?
What is Postulate 6?
Signup and view all the answers
What is Postulate 7?
What is Postulate 7?
Signup and view all the answers
What is Postulate 8?
What is Postulate 8?
Signup and view all the answers
What is Postulate 9?
What is Postulate 9?
Signup and view all the answers
What does the SSS Postulate state?
What does the SSS Postulate state?
Signup and view all the answers
What does the SAS Postulate indicate?
What does the SAS Postulate indicate?
Signup and view all the answers
What does the ASA Postulate state?
What does the ASA Postulate state?
Signup and view all the answers
What does Theorem 1-1 state?
What does Theorem 1-1 state?
Signup and view all the answers
What does Theorem 1-2 indicate?
What does Theorem 1-2 indicate?
Signup and view all the answers
What does Theorem 1-3 state?
What does Theorem 1-3 state?
Signup and view all the answers
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
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
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!