Geometry Chapter 1 Review Flashcards

Questions and Answers

What is perimeter?

Distance around an object

What is area?

Space inside an object

What types of units express perimeter?

Feet, inches, etc.

What types of units express area?

Square centimeters (cm^2) Signup and view all the answers

What is circumference?

Distance around the circle Signup and view all the answers

What is the Midpoint Formula?

M = ((x₁ + x₂)/2, (y₁ + y₂)/2) Signup and view all the answers

What is the Distance Formula?

d = √((x₁ - x₂)² + (y₁ - y₂)²) Signup and view all the answers

What does the Pythagorean Theorem state?

The sum of the squares of the legs equals the square of the hypotenuse. Signup and view all the answers

What is transformation in geometry?

A change in position, size, or shape of a figure Signup and view all the answers

What is a preimage?

The original figure Signup and view all the answers

What is an image in geometry?

The resulting figure after a transformation Signup and view all the answers

What happens during reflection in geometry?

A figure is flipped over a line Signup and view all the answers

What occurs during rotation?

A figure is turned around a fixed point Signup and view all the answers

What is a translation in geometry?

A figure is slid to a new position without turning Signup and view all the answers

What is a point in geometry?

Names a location and has no size, represented by a dot Signup and view all the answers

What is a line?

A straight path that has no thickness and extends forever Signup and view all the answers

What is a plane?

A flat surface that has no thickness and extends forever Signup and view all the answers

What is a segment?

The part of a line consisting of two points and all points between them Signup and view all the answers

What is an endpoint?

A point at one end of a segment or the starting point of a ray Signup and view all the answers

What is a ray?

Part of a line that starts at an endpoint and extends forever in one direction Signup and view all the answers

What are opposite rays?

Two rays that have a common endpoint and form a line Signup and view all the answers

What are collinear points?

Points that lie on the same line Signup and view all the answers

What are coplanar points?

Points that lie in the same plane Signup and view all the answers

What is a postulate (or axiom)?

A statement that is accepted as true without proof Signup and view all the answers

What is the distance between any two points?

The absolute value of the difference of the coordinates Signup and view all the answers

What is length in relation to distance?

The distance is also called length Signup and view all the answers

What are congruent segments?

Segments that have the same length Signup and view all the answers

What is a midpoint?

The point that bisects a segment into two congruent segments Signup and view all the answers

What are angles?

Formed by two rays with a common endpoint called the vertex Signup and view all the answers

What are congruent angles?

Angles that have the same measure Signup and view all the answers

What is an angle bisector?

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

What are adjacent angles?

Two angles that have a common vertex Signup and view all the answers

What is a linear pair?

Two adjacent angles whose noncommon sides are opposite rays Signup and view all the answers

What are complementary angles?

Two angles whose measures sum to 90 degrees Signup and view all the answers

What are supplementary angles?

Two angles whose measures sum to 180 degrees Signup and view all the answers

What are vertical angles?

Two nonadjacent angles formed by two intersecting lines Signup and view all the answers

Study Notes

Geometric Concepts

Perimeter: Total distance around a geometric figure; measured in linear units like feet or inches.
Area: The space contained within a two-dimensional shape; expressed in square units, e.g., cm².
Circumference: The perimeter specific to circles, representing the distance around a circle.

Formulas and Measurements

Midpoint Formula: For two points A(x₁, y₁) and B(x₂, y₂), the midpoint M is calculated as ( M = \left(\frac{x₁ + x₂}{2}, \frac{y₁ + y₂}{2}\right) ).
Distance Formula: The distance ( d ) between two points (x₁, y₁) and (x₂, y₂) is calculated using ( d = \sqrt{(x₁ - x₂)² + (y₁ - y₂)²} ).
Pythagorean Theorem: In right triangles, ( a² + b² = c² ), where c is the hypotenuse and a, b are the legs.

Transformations

Transformation: Refers to the change in position, size, or shape of a geometric figure.
Preimage: The original geometric figure before any transformation.
Image: The resulting figure after transformation.
Reflection: Flipping a figure over a specified line.
Rotation: Turning a figure around a fixed point.
Translation: Sliding a figure to a new position without rotation or resizing.

Basic Geometric Elements

Point: A precise location with no size, typically represented by a dot.
Line: A straight, infinite path with no thickness.
Plane: An infinitely extending flat surface without thickness.
Segment: A part of a line defined by two endpoints and includes all points between them.
Endpoint: A point marking the end of a segment or the start of a ray.
Ray: A portion of a line with one endpoint extending infinitely in one direction.
Opposite Rays: Two rays sharing a common endpoint forming a straight line.
Collinear Points: Points lying on the same straight line.
Coplanar Points: Points that exist within the same plane.

Geometric Postulates and Measurements

Postulate (or Axiom): A universally accepted statement or principle in geometry without requiring proof.
Distance: The absolute value of the difference between coordinates of two points; also referred to as length.
Congruent Segments: Segments that are identical in length.
Midpoint: The point dividing a segment into two equal parts, creating two congruent segments.

Angle Definitions

Angles: Formed by two rays that meet at a common endpoint called the vertex.
Congruent Angles: Angles that share the same measure.
Angle Bisector: A ray that divides an angle into two equal angles.
Adjacent Angles: Two angles that share a common vertex and side.
Linear Pair: Two adjacent angles whose non-common sides form opposite rays, summing to 180 degrees.
Complementary Angles: Two angles whose measures together equal 90 degrees.
Supplementary Angles: Two angles whose measures add up to 180 degrees.
Vertical Angles: Non-adjacent angles formed when two lines intersect, always equal in measure.

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Description

Test your understanding of essential geometry concepts with these flashcards focusing on chapter 1. Learn key terms such as perimeter, area, and circumference, along with their definitions. Ideal for students looking to review and reinforce their knowledge in geometry.