Unit 4 - GeomeTree - growing your knowledge in geometric shapes and solids

Side of an Angle

One of the rays, segments, or lines that form an angle.

Conics (curved shapes)

Plane shapes that have boundaries that are one continuous, curved lines and that can be formed by a cross-section of a cone or double cone. Circles and ellipses fall under this category of plane shapes.

Reflex Angle

The larger angle (greater than 180 and less than 360) as measured from outside of an acute, obtuse, or right angle.

Base of a Solid

The polygon or plane figure that is not the curved surface or lateral face of the solid.

Circles

The set of all points in a plane that are a given distance (radius) from a given point (center.)

Ellipse

The set of all points in a plane whose sum of distances from two set points (foci points) along its major axis is constant.

Sphere

The set of all points that are a given distance from a given point. It is a 3-dimensional figure.

Faces

the flat polygonal surfaces of a polyhedron

Platonic solids

A group of five polyhedron that are both convex and regular (all faces are congruent and all angles are congruent) where the same number of faces intersect at each vertex.

Rhombus

A parallelogram with four congruent sides (an equilateral parallelogram.)

Rectangle

A parallelogram with four right angles (an equiangular parallelogram.)

Vertex

A point that is the intersection of two segments, or two rays, at their endpoints. In an angle, the vertex is the point about which the angle is measured. In a shape, it is the corners of the sides or faces.

Concave Polygon

A polygon that has and interior angle that is greater than 180 (a reflex angle)

Convex Polygon

A polygon that has no interior angles greater than 180.

Equiangular Polygon

A polygon whose angles are all congruent.

Equilateral Polygon

A polygon whose sides are all congruent.

Octagon

A polygon with eight sides.

Pentagon

A polygon with five sides.

Quadrilateral

A polygon with four sides.

Nonagon

A polygon with nine sides.

Heptagon

A polygon with seven sides.

Hexagon

A polygon with six sides.

Decagon

A polygon with ten sides.

Triangle

A polygon with three sides.

Dodecagon

A polygon with twelve sides.

Line Segment

A portion of a line that has definite length, and two endpoints. Name the line segment by its two endpoints in any order.

Trapezoid

A quadrilateral with one pair of parallel sides (bases) and two legs.

Parallelogram

A quadrilateral with two pairs of parallel sides.

Square

A regular parallelogram. An equilateral rectangle. An equiangular rhombus.

Polyhedron

A solid shape with many plane faces made of polygons.

Oblique Solid

A solid whose height is shorter than the length of its axis(line between the two bases or the base and vertex).

Right Solid

A solid whose height is the same length as its axis (line between the two bases or the base and vertex).

Cone

A solid with a circular base and a curved lateral surface that meets in a vertex

Prism

A solid with congruent, parallel polygonal bases joined by rectangles or parallelograms.

Pyramid

A solid with one polygon base and triangular lateral faces that meet in one vertex.

Cylinder

A solid with two congruent, parallel circular bases joined by a curved lateral surface.

Isosceles Trapezoid

A trapezoid with congruent legs.

Scalene Triangle

A triangle whose sides are not congruent.

Equilateral Triangle

A triangle with all three sides congruent. (A regular triangle.)

Isosceles Triangle

A triangle with at least two congruent sides.

Obtuse Triangle

A triangle with one obtuse angle and two acute angles.

Right Triangle

A triangle with one right angle and two acute angles. The two acute angles are complementary.

Acute Triangle

A triangle with three acute angles.

Right Angle

An angle whose measure is 90 degrees. The sides of this angle are perpendicular.

Obtuse Angle

An angle whose measure is less than 180 but greater than 90 degrees.

Acute Angle

An angle whose measure is less than 90 degrees.

Regular Polygon

An equilateral and equiangular polygon - all sides are the same measure and all angles are the same measure.

Dimension

Length, width, or depth are three examples of dimension. We will study plane shapes with 2 dimensions and solid shapes with 3 dimensions.

edges

The intersection of faces of a 3-D figure

Polygon

A closed plane figure whose sides are line segments that intersect only at their endpoints. Name a polygon by its vertices in clockwise or counter-clockwise order, starting at any vertex.

Dart

A concave quadrilateral with two pairs of consecutive, congruent sides. No sides are parallel.

Kite

A convex quadrilateral with two pairs of consecutive, congruent sides. No sides are parallel.

Euler's Theorem

Faces + Vertices = Edges + 2

Congruent

Geometric shapes that are the same shape and have the same measure are congruent.

Measure of an angle

The amount of turning about the vertex from one side to the other. The measure of an angle is given in degrees or radians.

Angle

The inclination between two lines, rays, segments, or sides of a polygon. The measure of an angle is in units of degrees or radians.

Straight Angle

Two angle sides that make a straight line measuring 180 degrees.

Point

Undefined term in Euclidean Geometry. A location in space. No measure (length, width, depth). Zero dimension. Name a point with one upper case letter.

Plane

Undefined term in Euclidean Geometry. The straight path of a line as it travels in space. No depth. Infinite length and infinite width. Two dimensions. Name a plane with a capital letter.

Line

Undefined term in Euclidean Geometry. The straight path of a point as it travels in space. No width or depth. Infinite length. One dimension. Name a line with two points or one lower case script letter.