Geo Enriched test

Point

A location marked in space; has no size.

Line

Extends infinitely in both directions.

Ray

Has a starting point and extends infinitely in one direction.

Segment

Has two distinct endpoints.

Congruent segments

Segments that have the same length, marked with tick marks.

Parallel Lines

Lines that never intersect, depicted with arrows.

Perpendicular Lines

Lines that intersect at a right angle, marked with a right-angle box.

Angle Congruence

Angles that are equal, indicated with curved arcs.

Inductive Reasoning

Finding a pattern to predict a rule, e.g., observing a pattern in a sequence.

Deductive Reasoning

Using established rules to prove statements, e.g., the rule of linear pairs forming supplementary angles.

Conditional Statement

A statement of the form 'if p, then q.'

Converse Statement

The reverse of a conditional statement, 'if q, then p.'

Vertical Angles

Opposite angles formed by intersecting lines that are equal.

Linear Pair

Two adjacent angles that form a straight line; their sum is 180°.

Complementary Angles

Two angles whose sum is 90°.

Supplementary Angles

Two angles whose sum is 180°.

Angle Addition Postulate

States that the sum of the angles formed at a point equals the angle that they form together.

Segment Addition Postulate

If point B is between A and C, then AB + BC = AC.

Corresponding Angles

Pairs of angles that are in the same position relative to the parallel lines and transversal.

Alternate Interior Angles

Angles on opposite sides of the transversal but inside the parallel lines; they are equal.

Triangle Classification

Triangles can be classified as acute, right, or obtuse based on angle measures.

Isosceles Triangle

A triangle with at least two sides equal; base angles are congruent.

Triangle Angle Sum

The sum of the interior angles of a triangle is always 180°.

Triangle Exterior Angle Theorem

An exterior angle equals the sum of the two remote interior angles.

Congruence Theorems

Methods to prove triangles are congruent: SSS, SAS, ASA, AAS.

CPCTC

Corresponding Parts of Congruent Triangles are Congruent.

Triangle Inequality Theorem

In a triangle, the sum of any two sides must be greater than the third side.

Pythagorean Theorem

In a right triangle, a² + b² = c², where c is the hypotenuse.

Rigid Motions

Transformations that preserve size and shape: translations, reflections, and rotations.

Distance Formula

The formula for calculating the distance between two points (x1, y1) and (x2, y2) is √((x2 - x1)² + (y2 - y1)²).

Midpoint Formula

The midpoint of two points (x1, y1) and (x2, y2) is ((x1+x2)/2, (y1+y2)/2).

Parallelogram Properties

In a parallelogram, opposite sides are equal and parallel, and opposite angles are equal.

Rectangle Properties

A rectangle has right angles and equal diagonals.

Rhombus Properties

In a rhombus, all sides are equal, diagonals bisect each other at right angles.

Square Properties

A square has properties of both a rectangle and a rhombus.

Isosceles Trapezoid

A trapezoid with congruent legs and base angles.

Interior Angle Sum Formula

The sum of the interior angles of a polygon with n sides is (n-2) * 180°.

Area of Triangle

Area = 1/2 * base * height.

Area of Rectangle

Area = length * width.

Factoring Methods

Methods to simplify algebraic expressions: GCF, Trinomials, Difference of squares.

Systems of Equations

Methods to solve systems include substitution and elimination.

Multi-Step Equation Method

When solving multi-step equations with fractions, clear denominators first.