Geometry Basics and Angle Relationships

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Questions and Answers

What is an exact location in space?

point

What is a length made up of points that extends infinitely in both directions?

Line

What is a portion of a line having two endpoints?

line segment

What is a portion of a line having one endpoint and extending infinitely in one direction?

Ray Signup and view all the answers

What is formed by two rays that share a common endpoint?

An angle Signup and view all the answers

What is the common endpoint of an angle?

vertex Signup and view all the answers

What are two lines that cross at a point called?

Intersecting lines Signup and view all the answers

What are lines that never intersect called?

parallel lines Signup and view all the answers

What are intersecting lines that form four right angles called?

Perpendicular lines Signup and view all the answers

What is an angle between 0° and 90° called?

Acute angle Signup and view all the answers

What is a 90° angle called?

right angle Signup and view all the answers

What is an angle between 90° and 180° called?

obtuse angle Signup and view all the answers

What is a 180° angle called?

Straight Signup and view all the answers

What is an angle between 180° and 360° called?

Reflex Signup and view all the answers

What are two angles that have a common side between them and share a common vertex called?

Adjacent angles Signup and view all the answers

When two lines intersect, they form two pairs of opposite angles called _________

Vertical angles Signup and view all the answers

What are two angles whose sum is 90° called?

complementary angles Signup and view all the answers

What are two angles whose sum is 180° called?

supplementary angles Signup and view all the answers

What is any four-sided polygon called?

quadrilateral Signup and view all the answers

What is any quadrilateral that has only one set of opposite sides parallel called?

Trapezoid Signup and view all the answers

What is a quadrilateral that has both sets of opposite sides parallel called?

Parallelogram Signup and view all the answers

What is a parallelogram that has all equal sides called?

Rhombus Signup and view all the answers

What is a parallelogram that has four right angles called?

rectangle Signup and view all the answers

What is a rectangle that has all equal sides called?

Square Signup and view all the answers

What type of triangle has three acute angles?

Acute triangle Signup and view all the answers

What is a triangle with one obtuse angle called?

obtuse triangle Signup and view all the answers

What is a triangle with one right angle called?

right triangle Signup and view all the answers

What is a triangle with three equal sides called?

equilateral triangle Signup and view all the answers

What is a triangle with two equal sides called?

isosceles triangle Signup and view all the answers

What is a triangle with no equal sides called?

scalene triangle Signup and view all the answers

What is the formula for the area of a square?

A = s² Signup and view all the answers

What is the formula for the area of a parallelogram?

A = bh Signup and view all the answers

What is the formula for the area of a triangle?

A = ½bh Signup and view all the answers

What is the formula for the area of a trapezoid?

A = 1/2h(b1 + b2) Signup and view all the answers

What is a figure formed from combining two or more simple shapes called?

Complex figure Signup and view all the answers

What is the line drawn from the center to any point on the circle called?

Radius Signup and view all the answers

What is a line through the center with both ends on the circle called?

Diameter Signup and view all the answers

What is a line segment whose endpoints are on a circle called?

chord Signup and view all the answers

What is an arc that is equal to half a circle called?

Semicircle Signup and view all the answers

What is the part of a circle connecting two points on the circle called?

Arc Signup and view all the answers

What is the measure of the distance around a circle called?

circumference Signup and view all the answers

What is the formula for the area of a circle?

A = πr² Signup and view all the answers

What is the formula for the circumference of a circle?

C = 2πr or C = πd Signup and view all the answers

What is the value of Pi (π)?

3.14 Signup and view all the answers

What symbol means greater than?

<blockquote> </blockquote> Signup and view all the answers

What symbol means less than?

< Signup and view all the answers

What symbol means not equal to?

≠ Signup and view all the answers

What symbol means less than or equal to?

≤ Signup and view all the answers

What symbol means greater than or equal to?

≥ Signup and view all the answers

Study Notes

Geometry Basics

A point denotes an exact location in space.
A line is an infinite length formed by connecting points in both directions.
A line segment is a part of a line with two defined endpoints.
A ray has one endpoint and extends infinitely in one direction.

Angles and Lines

An angle is formed by two rays that share a common endpoint known as the vertex.
Intersecting lines cross each other at a single point, while parallel lines never cross.
Perpendicular lines intersect forming four right angles.

Types of Angles

An acute angle measures between 0° and 90°.
A right angle measures exactly 90°.
An obtuse angle is between 90° and 180°.
A straight angle measures 180°.
A reflex angle measures between 180° and 360°.

Angle Relationships

Adjacent angles share a common side and vertex.
Vertical angles are formed when two lines intersect, creating pairs of opposite angles.
Complementary angles sum to 90°.
Supplementary angles sum to 180°.

Quadrilaterals

A quadrilateral is any polygon with four sides.
A trapezoid has one pair of opposite sides parallel.
A parallelogram has both pairs of opposite sides parallel.
A rhombus is a parallelogram with all sides equal.
A rectangle is a parallelogram with four right angles.
A square is a rectangle with all sides equal.

Triangles

An acute triangle has three acute angles.
An obtuse triangle has one obtuse angle.
A right triangle contains one right angle.
An equilateral triangle features three equal sides.
An isosceles triangle has two equal sides.
A scalene triangle has no equal sides.

Area Formulas

Area of a square: ( A = s^2 )
Area of a parallelogram: ( A = bh )
Area of a triangle: ( A = \frac{1}{2}bh )
Area of a trapezoid: ( A = \frac{1}{2}h(b_1 + b_2) )

Circle Geometry

A radius connects the center of a circle to any point on its circumference.
A diameter is a line segment that passes through the center, with endpoints on the circle.
A chord is a line segment whose endpoints lie on the circle.
A semicircle is an arc that represents half of the circle.
An arc connects two points on the circumference of the circle.
Circumference measures the distance around a circle.

Circle Formulas

Area of a circle: ( A = \pi r^2 )
Circumference of a circle:
- ( C = 2\pi r )
- ( C = \pi d )
Pi (( \pi )) is approximately 3.14.

Inequalities

The symbol > denotes "greater than."
The symbol < indicates "less than."
The symbol ≠ signifies "not equal to."
The symbol ≤ means "less than or equal to."
The symbol ≥ means "greater than or equal to."

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Description

Explore the fundamentals of geometry, including points, lines, and various types of angles. Understand the relationships between different angles, including adjacent and vertical angles. This quiz will test your knowledge of these essential geometric concepts.