All Geometry Theorems Flashcards

Questions and Answers

What does 'congruent' mean?

A triangle with all sides equal

Two angles together add up to 180 degrees

Equal in size and shape (correct)

Lines that intersect at a 90 degree angle

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?

Lines that intersect at a 90 degree angle. Signup and view all the answers

What defines an isosceles triangle?

A triangle with two congruent sides. Signup and view all the answers

What are supplementary angles?

Angles that add up to 180 degrees. Signup and view all the answers

What are complementary angles?

Angles that add up to 90 degrees. Signup and view all the answers

What is a linear pair?

A pair of adjacent angles formed when two lines intersect. Signup and view all the answers

What is an angle bisector?

A ray that cuts an angle into two congruent angles. Signup and view all the answers

What is an altitude in a triangle?

A segment perpendicular from a vertex to the opposite side. Signup and view all the answers

What is a perpendicular bisector?

A line that is perpendicular to a side of a triangle and passes through the midpoint. Signup and view all the answers

What is a median in a triangle?

A segment from a vertex to the opposite side. Signup and view all the answers

What does the Ruler Postulate state?

Every point on a number line can be paired with a number and vice versa. Signup and view all the answers

What does the Segment Addition Postulate explain?

Adding two segments together creates a larger segment. Signup and view all the answers

What is the Protractor Postulate?

The extension of the Ruler Postulate with a protractor. Signup and view all the answers

What is the Angle Addition Postulate?

Two angles added together create one larger angle. Signup and view all the answers

What does the Addition Property state?

If a = b, then a + c = b + c. Signup and view all the answers

What does the Subtraction Property indicate?

If a = b, then a - c = b - c. Signup and view all the answers

What is the Multiplication Property?

If a = b, then a times c = b times c. Signup and view all the answers

What does the Division Property state?

If a = b, then a divided by c = b divided by c. Signup and view all the answers

What is the Substitution Property?

If a = b, then a can replace b in any expression. Signup and view all the answers

What does the Reflexive Property express?

A = A. Signup and view all the answers

What is the Symmetric Property?

If a = b, then b = a. Signup and view all the answers

What does the Transitive Property state?

If a = b and b = c, then a = c. Signup and view all the answers

What is the Distributive Property?

If a(b + c), then ab + ac. Signup and view all the answers

What is Postulate 5?

A line contains at least 2 points, a plane contains at least 3 points, and space contains at least 4 points. Signup and view all the answers

What is Postulate 6?

Through any two points, there is exactly one line. Signup and view all the answers

What is Postulate 7?

Through any three points, there is at least one plane. Signup and view all the answers

What is Postulate 8?

If two planes intersect, then their intersection is a line. Signup and view all the answers

What is Postulate 9?

If two planes intersect, then their intersection is a line. Signup and view all the answers

What does the SSS Postulate state?

If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent. Signup and view all the answers

What does the SAS Postulate indicate?

If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent. Signup and view all the answers

What does the ASA Postulate state?

If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent. Signup and view all the answers

What does Theorem 1-1 state?

If two lines intersect, then they intersect in exactly one point. Signup and view all the answers

What does Theorem 1-2 indicate?

Through a line and a point not on the line, there is exactly one plane. Signup and view all the answers

What does Theorem 1-3 state?

If two lines intersect, then exactly one plane contains the lines. 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.

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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!