Geometry Foundations and Concepts Review

Flashcards covering key definitions, diagram rules, angle pairs, undefined/defined terms, coordinate plane geometry, and perimeter/area formulas based on geometry lecture notes.

When interpreting a geometric diagram, which concepts can be assumed?

Straight lines and segments, collinearity, and intersections can be assumed.

When interpreting a geometric diagram, which geometric properties cannot be assumed?

Perpendicular or right angles, parallel lines, congruence, and exact scale cannot be assumed.

What is the definition of complementary angles?

Two angles whose sum of measures is $90^\circ$.

What is the definition of supplementary angles?

Two angles whose sum of measures is $180^\circ$.

What geometric relationship exists between angles that form a linear pair?

Linear pairs are supplementary.

How are perpendicular lines defined?

Two lines intersect to form a right angle.

If the measure of the larger of two complementary angles is five more than four times the measure of the smaller angle, what is the measure of the smaller angle?

The smaller angle measures $17^\circ$ (found by solving $x + 4x + 5 = 90$).

What are undefined terms in geometry, and which terms belong to this category?

Undefined terms are words, usually readily understood, that are not formally defined. In geometry, point, line, and plane are considered undefined terms.

What is the definition of a defined term in geometry?

Defined terms are terms that can be defined using undefined terms or/and defined terms.

How is a line defined and named in geometry?

A line is a connected straight path with no thickness that continues forever in both directions. It is named using two points on the line (e.g., line $AB$, line $BA$, $\overleftrightarrow{AB}$, or $\overleftrightarrow{BA}$) or a cursive letter at the end (e.g., line $l$).

How is a plane defined and named in geometry?

A plane is a flat surface with no thickness that continues forever in ALL directions. It is named using an uppercase letter in the corner (e.g., plane M) or three non-collinear points (e.g., plane ABC).

What is a line segment and how is it named?

A line segment is a portion of a line that has $2$ endpoints and contains an infinite number of points between them. It is named using its two endpoints with a bar symbol (e.g., segment $AB$, segment $BA$, $\overline{AB}$, or $\overline{BA}$).

What is a ray and what rule must be followed when naming it?

A ray is a portion of a line with $1$ endpoint that continues forever in one direction and contains an infinite number of points. It is named using its endpoint and one other collinear point, with the endpoint always listed as the first letter (e.g., ray $AB$ or $\overrightarrow{AB}$).

For triangle $ABC$ with vertices $A(1, -1)$, $B(5, -1)$, and $C(4, 3)$, what are the exact side lengths of $AB$ and $AC$?

Side $AB = 4$ and side $AC = 5$.

What is a geometric model?

A geometric model is a geometric figure that represents a real-world object.

What defines a convex polygon?

A polygon is convex if no line that contains a side of the polygon contains a point in the interior of the polygon.

What are the distinctions between an equiangular polygon, an equilateral polygon, and a regular polygon?

An equiangular polygon has all interior angles congruent; an equilateral polygon has all sides congruent; a regular polygon has all sides congruent and all angles congruent.

What is the definition of a circle?

A circle is a set of coplanar points with the same distance to a fixed point called the center of the circle.

What are the perimeter and area formulas for a square, rectangle, and circle?

Square: $P = 4s$ and $A = s^2$; Rectangle: $P = 2l + 2w$ and $A = lw$; Circle: $C = \pi d = 2\pi r$ and $A = \pi r^2$.