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Definition: A pair of opposite rays are two rays that have the same endpoint and extend in opposite directions. Together, they form a line.
Notation: Ray BA and Ray BC

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A pair of opposite rays are two rays that have the same endpoint and extend in opposite directions.

Example: Ray CG and  Ray CD below

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Perpendicular means "at right angles". A line meeting another at a right angle, or 90° is said to be perpendicular to it.
In the diagram below, line u is perpendicular to line t.

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Definition: A point is a location. It has no size i.e. no width, no length and no depth.

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Definition: a line: • is straight (no curves), • has no thickness, and. • extends in both directions without end (infinitely).

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Definition: A ray is a line with an endpoint that extends infinitely in ONE direction.

Example: Ray ST

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A ray is named with two capital letters labeling the endpoint and the point the ray extends through, with a line over the letters that has ONE arrow only above the point the line extends through. Note that we would not call the ray below Ray DA or DC because it extends in the opposite direction.

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Definition: A line segment is a part of a line that is bounded by two distinct end points, and contains every point on the line between its endpoints.

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Example: Ray AB

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Definition: an angle that measures 90°, as in a corner of a square or at the intersection of two perpendicular straight lines.

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Congruent means the same shape and size.

We use congruence to talk about segments, angles, circles, triangles, quadrilaterals, and other polygons that are the same size and shape.

Two shapes are congruent when you can Turn,  and/or Slide one so it fits exactly on the other.

Triangle ABC and Triangle XYZ in the picture are congruent.

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A circle is a shape with all points the same distance from its center.

The radius r is the distance from the center to any point on the outside of the circle.
The diameter d is the distance across the circle at its widest point, or through the center.
The circumference C is the distance around the outside of the circle.

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An angle is the amount of turn between two directions.

It is formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

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Definition: parallel lines are lines in a plane which do not meet; that is, two lines in a plane that do not intersect or touch each other at any point are said to be parallel.

Notation: line AB || line CD
(in the diagram below)

The symbol || means parallel.

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Definition:a plane is a flat, two-dimensional surface that extends infinitely far.

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Exactly equal in size and shape.

Example: Angle A is congruent to angle B

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A line is said to be perpendicular to another line if the two lines intersect at a right angle.
Example: pink line and blue line below

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Line A ⊥ Line D
We read this "Line A is perpendicular to Line D"

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Two lines that continue indefinitely and will never meet
Notation: line MN || line OP

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We name circles by the capital letter that tells us the point in the center of the circle.

Example: The circle below is named Circle O.

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We name a plane by listing 3 points that lie on the plane, but are not collinear (you couldn't draw a straight line through all three of them).

Examples:
The blue plane below could be named plane ADC or plane DCB. But we would not name it plane ADB because points A, D, and B lie in a straight line.

The yellow plane below could be named plane EDB or plane ADG.
But we would not name it plane ADB because points A, D, and B lie in a straight line.

Notice that if you told someone to look at plane ADB, they wouldn't be sure whether you meant the blue one or the yellow one. That's why we don't use 3 collinear points to name a plane.

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A line is named with two capital letters labeling points on the line, with a line above the letters that has arrows on BOTH SIDES.
See the bottom figure and notation in the picture below.

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A line segment is named with two capital letters labeling the endpoints on the line, with a line above the letters that has NO ARROWS (since it doesn't extend forever in either direction).
See the top figure and notation in the picture below.

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An angle is named with 3 capital letters labeling points on the rays and the vertex, with the vertex in the MIDDLE of the name.

Notice that the angle below is NOT named angle CBA or angle ABC. The vertex A must be in the middle of the name.

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We use a lowercase letter m to stand for "measurement" in front of the name of the angle.
It looks like m<ABC = 90 degrees.

See the row named "Angle Measure" in the diagram below.

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The symbol below means "congruent". We use it the same way we would use an equal sign to say that two quantities are equal.
For example, angle A ≅ angle B is read as "Angle A is congruent to Angle B".

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We name a point with one capital letter.
Example: Point P or Point M