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# Geometry Chapter 5 Flashcards

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@DistinctiveDrama

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?

<p>Inside angles that lie on opposite sides of the transversal. These pairs of angles are congruent.</p> Signup and view all the answers

### What is a converse?

<p>The converse of a theorem is formed when the parts of the theorem are reversed.</p> Signup and view all the answers

### What are corresponding angles?

<p>Angles that are in the same position on two parallel lines in relation to a transversal. These pairs of angles are congruent.</p> Signup and view all the answers

### What is deductive reasoning?

<p>A system of reasoning that uses facts, rules, definitions, or properties to reach logical conclusions.</p> Signup and view all the answers

### What does 'equiangular' mean?

<p>A polygon in which all angles are congruent.</p> Signup and view all the answers

### What are exterior angles?

<p>The four outer angles formed by two parallel lines cut by a transversal.</p> Signup and view all the answers

### What is a formal proof?

<p>A two-column proof containing statements and reasons.</p> Signup and view all the answers

### What is a hypotenuse?

<p>The side opposite the right angle in a right triangle.</p> Signup and view all the answers

### What is inductive reasoning?

<p>Reasoning that uses a number of specific examples to arrive at a plausible generalization or prediction.</p> Signup and view all the answers

### What is an informal proof?

<p>A paragraph proof.</p> Signup and view all the answers

### What are interior angles?

<p>The four inside angles formed by two parallel lines cut by a transversal.</p> Signup and view all the answers

### What are legs in a right triangle?

<p>The two sides of a right triangle that form the right angle.</p> Signup and view all the answers

### What is a paragraph proof?

<p>A paragraph that explains why a statement or conjecture is true.</p> Signup and view all the answers

### What are parallel lines?

<p>Lines in the same plane that never intersect or cross.</p> Signup and view all the answers

### What are perpendicular lines?

<p>Two lines that intersect to form right angles.</p> Signup and view all the answers

### What is a polygon?

<p>A simple closed figure formed by three or more line segments (a many-sided figure).</p> Signup and view all the answers

### What is a proof?

<p>A logical argument in which each statement that is made is supported by a statement that is accepted as true.</p> Signup and view all the answers

### What is the Pythagorean Theorem?

<p>In a right triangle, the square of the length of the hypotenuse c is equal to the sum of the squares of the lengths of the legs a and b.</p> Signup and view all the answers

### What is a regular polygon?

<p>A polygon that is equilateral and equiangular.</p> Signup and view all the answers

### What are remote interior angles?

<p>The angles of a triangle that are not adjacent to a given exterior angle.</p> Signup and view all the answers

### What is a theorem?

<p>A statement or conjecture that can be proven.</p> Signup and view all the answers

### What is a transversal?

<p>A line that intersects two or more other lines.</p> Signup and view all the answers

### What is a triangle?

<p>A figure formed by three line segments that intersect only at their endpoints (a three-sided polygon).</p> Signup and view all the answers

### What is a two-column proof?

<p>A formal proof that contains statements and reasons organized in two columns. Each step is called a statement, and the properties that justify each step are called reasons.</p> 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.

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## 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.

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