Basic Concepts in Geometry and Algebra

Study Notes

Basic Concepts in Geometry and Algebra

Points identify specific locations on a plane, represented by capital letters, and have no size.
Line Segments connect two endpoints, having a definite length, denoted by the endpoints.
A Ray or Vector starts at a point and extends infinitely in one direction, characterized by an initial point and an arrowhead.

Perpendicular Lines and Angles

Perpendicular Lines intersect to create four equal angles, forming a right angle (90º).
An Angle is created when two rays or line segments meet at a point, known as the vertex.

Types of Angles

A Straight Angle measures exactly 180º, with its rays forming a straight line.
Acute Angles measure less than 90º, indicating sharpness.
Obtuse Angles range from greater than 90º to less than 180º.
Reflex Angles exceed 180º but fall below 360º (e.g., 270º).

Triangles

A Triangle is a closed planar figure made of three line segments, having three sides and three angles; the angles always sum to 180º.

Types of Triangles

A Right Triangle includes one 90º angle, with two legs forming the right angle and the third side, the hypotenuse.
An Isosceles Triangle has two equal sides, and the angles opposite those sides are also equal.
An Isosceles Right Triangle combines traits of both, with two equal sides and a right angle.
An Equilateral Triangle features three equal sides and corresponding angles that are also equal.

Angle Relationships

An Exterior Angle is equal to the sum of the two opposite interior angles in a triangle.
Complementary Angles add up to 90º.
Supplementary Angles total 180º.

Triangle Theorems

SSS (Side, Side, Side): If three sides of one triangle match three sides of another, the triangles are congruent.
SAS (Side, Angle, Side): Two sides and the included angle of one triangle equal those of another triangle.
ASA (Angle, Side, Angle): Two angles and the included side correspond, resulting in congruency.
AAS (Angle, Angle, Side): If two angles and a non-included side of one triangle match the same parts of another triangle, they are congruent.
RHS (Right angle, Hypotenuse side): This theorem applies to right triangles to establish congruence.

Special Triangle Properties

Legs are the two shorter sides that meet at the right angle in a right triangle.
The Hypotenuse is the longest side, located opposite the right angle.

Pythagorean Theorem

This theorem states that in a right triangle, the sum of the squares of the legs equals the square of the hypotenuse (a² + b² = c²).

Description

This quiz covers essential concepts in geometry and algebra, including points, lines, angles, and triangles. Test your understanding of how these fundamental elements interact and their properties. Perfect for students seeking to reinforce their geometric and algebraic skills.