Questions and Answers
What does 'adjacent' mean?
Sharing a common side without overlapping
What does 'congruent' mean?
Same size and same shape
What are alternate exterior angles?
Outside angles that lie on opposite sides of the transversal. These pairs of angles are congruent.
What are alternate interior angles?
Signup and view all the answers
What is a converse?
Signup and view all the answers
What are corresponding angles?
Signup and view all the answers
What is deductive reasoning?
Signup and view all the answers
What does 'equiangular' mean?
Signup and view all the answers
What are exterior angles?
Signup and view all the answers
What is a formal proof?
Signup and view all the answers
What is a hypotenuse?
Signup and view all the answers
What is inductive reasoning?
Signup and view all the answers
What is an informal proof?
Signup and view all the answers
What are interior angles?
Signup and view all the answers
What are legs in a right triangle?
Signup and view all the answers
What is a paragraph proof?
Signup and view all the answers
What are parallel lines?
Signup and view all the answers
What are perpendicular lines?
Signup and view all the answers
What is a polygon?
Signup and view all the answers
What is a proof?
Signup and view all the answers
What is the Pythagorean Theorem?
Signup and view all the answers
What is a regular polygon?
Signup and view all the answers
What are remote interior angles?
Signup and view all the answers
What is a theorem?
Signup and view all the answers
What is a transversal?
Signup and view all the answers
What is a triangle?
Signup and view all the answers
What is a two-column proof?
Signup and view all the answers
Study Notes
Key Terms and Definitions
- Adjacent: Refers to two geometric figures or angles that share a common side without overlapping.
- Congruent: Indicates figures that are identical in size and shape.
- Alternate Exterior Angles: Pairs of congruent angles located outside two parallel lines and on opposite sides of a transversal.
- Alternate Interior Angles: Pairs of congruent angles found inside two parallel lines on opposite sides of a transversal.
- Converse: A restructured theorem formed by reversing the earlier components of the original theorem.
- Corresponding Angles: Angles that occupy the same relative position at the intersection of a transversal with two parallel lines; these angles are congruent.
- Deductive Reasoning: A logical reasoning approach that utilizes established facts, definitions, or properties to produce a logical conclusion.
- Equiangular: Refers to a polygon with all angles congruent to each other.
- Exterior Angles: The four angles located outside of two parallel lines that are intersected by a transversal.
- Formal Proof: A structured two-column proof consisting of statements and corresponding reasons supporting those statements.
Triangle Geometry Concepts
- Hypotenuse: The longest side of a right triangle, positioned opposite the right angle.
- Inductive Reasoning: A reasoning method that formulates a general conclusion based on specific examples or patterns observed.
- Informal Proof: Generally takes the form of a paragraph that articulates why a particular conjecture or statement is valid.
- Interior Angles: The four angles situated within the region defined by two parallel lines intersected by a transversal.
- Legs: The two sides of a right triangle that create the right angle.
- Paragraph Proof: A coherent paragraph that justifies the truth of a statement or conjecture through logical reasoning.
Geometric Properties
- Parallel Lines: Lines that exist within the same plane yet never meet or intersect.
- Perpendicular Lines: Lines that cross to form right angles, indicating a 90-degree intersection.
- Polygon: A closed geometric figure characterized by three or more connected line segments, also termed as a many-sided figure.
- Proof: A logical discourse in which statements made are substantiated by recognized true statements.
- Pythagorean Theorem: A fundamental relation in right triangles: the square of the hypotenuse lengths (c) equals the sum of the squares of the other two sides (a and b).
- Regular Polygon: A type of polygon that is both equilateral (all sides equal) and equiangular (all angles equal).
- Remote Interior Angles: Angles in a triangle that are not directly adjacent to a given exterior angle.
- Theorem: A declarative statement that can be rigorously proven based on previously established theorems or axioms.
- Transversal: A line that crosses two or more other lines, often creating various angles.
- Triangle: A geometric shape composed of three line segments that connect only at their endpoints.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Test your knowledge of key terms and concepts in Geometry Chapter 5, which focuses on triangles and the Pythagorean Theorem. This set of flashcards includes definitions and examples for important vocabulary such as adjacent, congruent, and alternate angles.