Introduction to Geometry

Flashcards covering key concepts in Geometry including definitions, properties, and fundamental theorems.

What is Geometry?

A branch of mathematics that studies shapes, sizes, positions of figures, and the properties of space.

What are the Greek roots of the word 'geometry'?

The word 'geometry' comes from 'geo' (earth) and 'metron' (measurement).

List some applications of Geometry.

Architecture, Engineering, Art, Design, Computer Graphics, Gaming, Navigation, Surveying, Science, and Problem-Solving.

What is a point in geometry?

A fundamental element that has no dimension, represented by a dot and labeled with a capital letter.

Define a line in geometry.

A one-dimensional figure that extends infinitely in both directions, defined by at least two points.

What is a plane in geometry?

A two-dimensional flat surface that extends infinitely in all directions, defined by at least three non-collinear points.

What is an acute angle?

An angle that measures greater than 0° and less than 90°.

What is the measure of a right angle?

Exactly 90°.

What is a straight angle?

An angle that measures exactly 180°.

Define complementary angles.

Two angles whose measures add up to 90°.

What is a ray?

A part of a line that has one endpoint and extends infinitely in one direction.

Define parallel lines.

Two or more lines in the same plane that never intersect.

What is a transversal?

A line that intersects two or more other lines at distinct points.

What are vertical angles?

Two non-adjacent angles formed by the intersection of two lines, which are always congruent.

What is a polygon?

A closed plane figure formed by three or more line segments called sides.

Define a regular polygon.

A polygon in which all sides and all interior angles are congruent.

What is the sum of interior angles of a polygon with n sides?

(n−2)×180°.

What is the Pythagorean Theorem?

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

What is a trapezoid?

A quadrilateral with exactly one pair of parallel sides.

Define the circumference of a circle.

The distance around the circle, calculated as C=2πr or C=πd.

What is the area of a circle?

The space enclosed by the circle, calculated as A=πr².

What defines congruent triangles?

Two triangles that have the same size and shape, with all corresponding sides and angles congruent.

What is the sum of the measures of the angles in any triangle?

Always 180°.

What distinguishes similar triangles?

Two triangles with the same shape but not necessarily the same size, with corresponding angles congruent and sides proportional.