# data[].attributes.body
a ray is a line with a single endpoint (or point of origin) that extends infinitely in one direction.

# data[].attributes.body
https://study.com/academy/lesson/what-is-a-ray-in-geometry-definition-examples.html

# data[].attributes.body
A point is shown by a dot. A line is defined as a line of points that extends infinitely in two directions. It has one dimension, length.

# data[].attributes.body
the space (usually measured in degrees) between two intersecting lines or surfaces at or close to the point where they meet.

# data[].attributes.body
https://www.mathplanet.com/education/geometry/points.../an-introduction-to-geometry

# data[].attributes.body
a long, narrow mark or band.

# data[].attributes.body
https://www.dictionary.com/browse/line

# data[].attributes.body
a part of a line that is bounded by two distinct end points

# data[].attributes.body
https://en.wikipedia.org/wiki/Line_segment

# data[].attributes.body
https://www.dictionary.com/browse/angle

# data[].attributes.body
please find a video using the "Google magnifying glass icon" and complete pads for:
Plane
Parallel lines
Intersecting Lines
Vertex

Also for Collinear and
Coplanar (unless you choose Google Slides)

# data[].attributes.body
please find a video using the "Google magnifying glass icon" and complete pads for:
Plane
Parallel lines
Intersecting Lines
Vertex

Also for Collinear and
Coplanar (unless you choose Google Slides)

# data[].attributes.body
please find a video using the "Google magnifying glass icon" and complete pads for:
Plane
Parallel lines
Intersecting Lines
Vertex

Also for Collinear and
Coplanar (unless you choose Google Slides)

# data[].attributes.body
please find a video using the "Google magnifying glass icon" and complete pads for:
Plane
Parallel lines
Intersecting Lines
Vertex

Also for Collinear and
Coplanar (unless you choose Google Slides)

# data[].attributes.body
please find a video using the "Google magnifying glass icon" and complete pads for:
Plane
Parallel lines
Intersecting Lines
Vertex

Also for Collinear and
Coplanar (unless you choose Google Slides)

# data[].attributes.body
a measurable extent of some kind, such as length, breadth, depth, or height.

# data[].attributes.body
https://www.dictionary.com/browse/dimension

# data[].attributes.attachment_link.title
Math Mornings at Yale: Higher Dimensional Space and the Things In It

# data[].attributes.body
the continuous line forming the boundary of a closed geometric figure.

# data[].attributes.body
https://www.dictionary.com/

# data[].attributes.body
Area is the quantity that expresses the extent of a two-dimensional figure or shape, or planar lamina, in the plane. Surface area is its analog on the two-dimensional surface of a three-dimensional object.

# data[].attributes.body
https://en.wikipedia.org/wiki/Area

# data[].attributes.body
a solid geometric figure whose two end faces are similar, equal, and parallel rectilinear figures, and whose sides are parallelograms.

# data[].attributes.body
https://www.dictionary.com/browse/prism

# data[].attributes.attachment_link.title
3.5 Prims and Kruskals Algorithms - Greedy Method

# data[].attributes.body
a solid geometric figure with straight parallel sides and a circular or oval cross section.

# data[].attributes.body
https://www.merriam-webster.com/dictionary/prism

# data[].attributes.attachment_link.title
Surface area and volume of a cylinder - (CBSE Grade: 08 Maths)

# data[].attributes.body
a surface or solid figure generated by the straight lines that pass from a circle or other closed curve to a single point (the vertex) not in the same plane as the curve. A cone with the vertex perpendicularly over the center of a circular base is a right circular cone.

# data[].attributes.body
https://en.wikipedia.org/wiki/Cone

# data[].attributes.body
a polyhedron of which one face is a polygon of any number of sides, and the other faces are triangles with a common vertex.

# data[].attributes.body
https://www.mathopenref.com/pyramid.html

# data[].attributes.body
a round solid figure, or its surface, with every point on its surface equidistant from its center

# data[].attributes.body
https://www.mathsisfun.com/geometry/sphere.html

# data[].attributes.body
the outside part or uppermost layer of something (often used when describing its texture, form, or extent).

# data[].attributes.body
each of the pairs of opposite angles made by two intersecting lines.

# data[].attributes.body
(of a line) intersecting a system of lines.

# data[].attributes.body
are formed when a transversal passes through two lines.

# data[].attributes.attachment_link.description
The surface area of a solid object is a measure of the total area that the surface of the object occupies. The mathematical definition of surface area in the presence of curved surfaces is considerably more involved than the definition of arc length of one-dimensional curves, or of the surface area for polyhedra (i.e., objects with flat polygonal faces), for which the surface area is the sum of the areas of its faces.

# data[].attributes.attachment_link.readable_text
"Vertical" in this case means they share the same Vertex (corner point), not the usual meaning of up-down.

Example: a° and b° are vertical angles.

The interesting thing here is that vertical angles are equal:

a° = b°

(in fact they are congruent angles)

Have a play with them yourself. Notice how the 4 angles are actually two pairs of "vertical angles":

images/geom-vert-angles.js

Example: Find angles a°, b° and c° below:

Because b° is vertically opposite 40°, it must also be 40°

A full circle is 360°, so that leaves 360° − 2×40° = 280°

Angles a° and c° are also vertical angles, so must be equal, which means they are 140° each.

Answer: a = 140°, b = 40° and c = 140°.

# data[].attributes.attachment_link.description
"Vertical" in this case means they share the same Vertex (corner point), not the usual meaning of up-down. The interesting thing here is that vertical angles are equal: a° = b° (in fact they are congruent angles) Have a play with them yourself.

# data[].attributes.attachment_link.readable_text
When two lines are crossed by another line (called the Transversal):

Alternate Interior Angles are a pair of angles on the inner side of each of those two lines but on opposite sides of the transversal.

In this example, these are two pairs of Alternate Interior Angles:

And

To help you remember: the angle pairs are on Alternate sides of the Transversal, and they are on the Interior of the two crossed lines.

Parallel Lines

When the two lines being crossed are Parallel Lines the Alternate Interior Angles are equal.
(Click on "Alternate Interior Angles" to have them highlighted for you.)

# data[].attributes.attachment_link.description
Learn about Alternate Interior Angles: When two lines are crossed by another line (called the Transversal), Alternate Interior Angles are a pair of angles on the inner side of each of those two lines but on opposite sides of the transversal.

# data[].attributes.attachment_link.title
Total Surface Area - the trick to getting it right

# data[].attributes.attachment_link.title
Vertical Angles - MathHelp.com - Geometry Help

# data[].attributes.attachment_link.title
Angles Formed by a Transversal with Two Parallel Lines | Don't Memorise

# data[].attributes.attachment_link.title
Alternate Interior Angles, Alternate Exterior Angles, Vertical Angles, Corresponding Angles

# data[].attributes.body
are two angles that are on theexterior.

# data[].attributes.body
When a line (called a transversal) intersects a pair of parallel lines,

# data[].attributes.body
that have a common vertex and a common side.

# data[].attributes.body
A linear pair is a pair of adjacent angles formed when two lines intersect. In the figure, and form a linear pair. So do and , and , and and .

# data[].attributes.body
This is a right angle. There's also a word for two angles whose sum add up to 90 degrees,

# data[].attributes.attachment_link.title
Alternate Exterior Angles definition - Math Open Reference

# data[].attributes.attachment_link.description
Definition and properties of alternate exterior angles, showing the pairs of angles associated with a transversal

# data[].attributes.attachment_link.readable_text
When two lines are crossed by another line (called the Transversal):

The angles in matching corners are called Corresponding Angles.

Parallel Lines

When the two lines being crossed are Parallel Lines the Corresponding Angles are equal.
(Click on "Corresponding Angles" to have them highlighted for you.)

# data[].attributes.attachment_link.description
When two lines are crossed by another line (called the Transversal): The angles in matching corners are called Corresponding Angles. When the two lines being crossed are Parallel Lines the Corresponding Angles are equal. (Click on "Corresponding Angles" to have them highlighted for you.)

# data[].attributes.attachment_link.readable_text
Two angles are Adjacent when they have a common side and a common vertex (corner point) and don't overlap.

Angle ABC is adjacent to angle CBD

Because:

they have a common side (line CB)

they have a common vertex (point B)

What Is and Isn't an Adjacent Angle

These ARE Adjacent Angles

they share a vertex and a side

NOT Adjacent Angles

they only share a vertex, not a side

NOT Adjacent Angles

they only share a side,
not a vertex

Don't Overlap!

ALSO the angles must not overlap.

NOT Adjacent Angles

angles a and b overlap

# data[].attributes.attachment_link.description
Two angles are Adjacent when they have a common side and a common vertex (corner point) and don't overlap. Angle ABC is adjacent to angle CBD Because: they have a common side (line CB) they have a common vertex (point B) These ARE Adjacent Angles they share a vertex and a side NOT Adjacent Angles they only share a vertex, not a side NOT Adjacent Angles they only share a side, not a vertex ALSO the angles must not overlap.

# data[].attributes.attachment_link.title
Linear Pair - math word definition - Math Open Reference

# data[].attributes.attachment_link.description
Definition and properties of a linear pair of angles - two angles that are adjacent and supplementary

# data[].attributes.attachment_link.readable_text
Two angles are Complementary when they
add up to 90 degrees (a Right Angle )

These two angles (40° and 50°) are Complementary Angles, because they add up to 90°:

Notice that together they make a right angle

But the angles don't have to be together.

These two are complementary because 27° + 63° = 90°

Play With It ...

(Drag the points)

images/geom-comp-supp.js?mode=comp

Right Angled Triangle

In a right angled triangle, the two non-right angles are complementary, because in a triangle the three angles add to 180°, and 90° has already been taken by the right angle.

When two angles add to 90°, we say they "Complement" each other.

Complementary comes from Latin completum meaning "completed" ...
because the right angle is thought of as being a complete angle.

Spelling: be careful, it is not "Complimentary Angle" (with an "i") ...
that would be an angle you get for free!

Complementary vs Supplementary

A related idea is Supplementary Angles - those add up to 180°

How to remember which is which? Well, alphabetically they are:

Complementary add to 90°

Supplementary add to 180°

You can also think:

"C" of Complementary is for "Corner" (a Right Angle), and

"S" of Supplementary is for "Straight" (180° is a straight line)

Or you can think:

when you are right you get a compliment (sounds like complement)

"supplement" (like a vitamin supplement) is something extra, so is bigger

5231, 5233, 819, 2109, 820, 2110, 5240, 9063, 3305, 3306

# data[].attributes.attachment_link.description
Two angles are Complementary when they add up to 90 degrees (a Right Angle )

# data[].attributes.attachment_link.title
Alternate interior and exterior angles - proof

# data[].attributes.attachment_link.title
Angles in parallel lines- corresponding angles

# data[].attributes.attachment_link.title
Complementary and supplementary angles | Angles and intersecting lines | Geometry | Khan Academy

# data[].attributes.body
either of two angles whose sum is 180°

# data[].attributes.attachment_link.readable_text
These two angles (140° and 40°) are Supplementary Angles, because they add up to 180°:

Notice that together they make a straight angle.

But the angles don't have to be together.

These two are supplementary because
60° + 120° = 180°

Play With It ...

(Drag the points)

images/geom-comp-supp.js?mode=supp

When the two angles add to 180°, we say they "Supplement" each other. comes from Latin supplere, to complete or "supply" what is needed

Complementary vs Supplementary

A related idea is Complementary Angles, they add up to 90°

How to remember which is which? Well, alphabetically they are:

Complementary add to 90°

Supplementary add to 180°

You can also think:

"C" of Complementary is for "Corner" (a Right Angle), and

"S" of Supplementary is for "Straight" (180° is a straight line)

Or you can think:

when you are right you get a compliment (sounds like complement)

"supplement" (like a vitamin supplement) is something extra, so is bigger

817, 1804, 5232, 5234, 818, 3303, 1805, 3304, 5235, 5236

# data[].attributes.attachment_link.description
These two angles (140° and 40°) are Supplementary Angles, because they add up to 180°: Notice that together they make a straight angle. But the angles don't have to be together. These two are supplementary because 60° + 120° = 180° (Drag the points) images/geom-comp-supp.js?mode=supp When the two angles add to 180°, we say they "Supplement" each other.

# data[].attributes.attachment_link.title
Complementary and supplementary angles | Angles and intersecting lines | Geometry | Khan Academy

# data[].attributes.body
of a surface or line) be inclined from a horizontal or vertical line; slant up or down.

# data[].attributes.attachment_link.title
Finding the Slope of a Line from the Graph 2 | Coolmath.com

# data[].attributes.attachment_link.description
Check it out: Let's find the slope of this line: