Definition: A shape, formed by two lines or rays diverging from a common point (the vertex).

Try this Adjust the angle below by dragging the orange dot.

Acute angleFrom Latin: acutus - "sharp, pointed"

Definition: An angle whose measure is less than 90°

Try this Adjust the angle below by dragging an orange dot and see how the angle ∠ABC behaves. Note that it is acute for all angles from zero to (but not including) 90°

Acute angles are the smallest, being between (but not including) zero and 90° Note also that acute triangles are those where all the interior angles are acute.

A way to remember

Sometimes we can confuse acute and obtuse angles. A way to remember is that small things tend to be cute. Acute angle is the smallest type.

Types of angleAltogether, there are six types of angle as listed below. Click on an image for a full description of that type and a corresponding interactive applet. 

Acute angleLess than 90°

Right angleExactly 90°

Obtuse angleBetween 90° and 180°

Straight angleExactly 180°

Reflex angleBetween 180° and 360°

Full angleExactly 360°

Names of Angles

As the Angle Increases, the Name Changes

Type of Angle Description

Acute Angle an angle that is less than 90°

Right Angle an angle that is 90° exactly

Obtuse Angle an angle that is greater than 90° but less than 180°

Straight Angle an angle that is 180° exactly

Reflex Angle an angle that is greater than 180°

Try It Yourself!

View Larger

 

In One Diagram

This diagram might make it easier to remember:

Also: Acute, Obtuse and Reflex are in alphabetical order.  

Be Careful What You Measure

This is an Obtuse Angle. And this is a Reflex Angle. 

But the lines are the same ... so when naming the angles make sure 

that you know which angle is being asked for!

Positive and Negative Angles

When measuring from a line:

a positive angle goes counterclockwise (opposite direction that clocks go)

a negative angle goes clockwise

Example: −67°

 

 

Parts of an Angle

The corner point of an angle is called the vertex

And the two straight sides are called arms

The angle is the amount of turn between each arm.

 

Labelling Angles

There are two main ways to label angles:

1. by giving the angle a name, usually a lower-case letter

like a or b, or sometimes a Greek letter like α (alpha)

or θ (theta)

2. or by the three letters on the shape that define the

angle, with the middle letter being where the angle

actually is (its vertex).

Example angle "a" is "BAC", and angle "θ" is "BCD"

 

Question   1  Question   2  Question   3  Question   4  Question   5 Question   6  Question   7  Question   8  Question   9  Question   10   

ShapeFrom Wikipedia, the free encyclopedia

This article is about describing the shape of an object. For common shapes, see list of geometric shapes. For

other uses, see Shape (disambiguation).

The shape of an object located in some space is a geometrical description of the part of that space occupied

by the object, as determined by its external boundary – abstracting from location and orientation in space, size,

and other properties such as colour, content, and material composition.

Mathematician and statistician David George Kendall writes:[1]

In this paper ‘shape’ is used in the vulgar sense, and means what one would normally expect it to mean. [...]

We here define ‘shape’ informally as ‘all the geometrical information that remains when location, scale[2] and

rotational effects are filtered out from an object.’

Simple shapes can be described by basic geometry objects such as a set of two or more points, a line, a curve,

a plane, a plane figure (e.g. square or circle), or a solid figure (e.g. cube orsphere). Most shapes occurring in

the physical world are complex. Some, such as plant structures and coastlines, may be so arbitrary as to defy

traditional mathematical description – in which case they may be analyzed by differential geometry, or

as fractals.

Two-Dimensional more ...

A shape that only has two dimensions (such as width and height) and no thickness.

Squares, Circles, Triangles, etc are two dimensional objects

G&M - 15 Three-dimensional shapes: See Table 15.1 for descriptions and examples of three-dimensional shapes used throughout the NECAP GLEs.

Table 15.1 – Three dimensional figures:

Figure Description Examples

Prism A prism is a three-dimensional figure with two parallel congruent faces, called bases, and lateral faces in the shape of parallelograms. Prisms are named according to the shape of their bases.

Right Hexagonal Prism

Rectangular prism

A prism whose bases and lateral faces are rectangles.

Cube A rectangular prism whose faces are squares.

Triangular prism

A prism whose bases are triangles

Cylinder A three-dimensional shape with two parallel congruent circular faces whose cross sections (taken parallel to these circular faces) are circular.

Cone A cone is like a pyramid with a circular base. (See Pyramid.)

Sphere A sphere is the set of all points in space that are a fixed distance from a common point called the center.

Pyramids A three-dimensional shape with one polygonal base and lateral faces the shape of triangles that meet at a common vertex, called the apex.

Example 15.1 – Applies properties to describe three-dimensional shapes:

Below is a triangular prism. Which of the following describes the triangular prism?

A) All faces are congruent.B) Because it has two triangles as bases, it has six edges.C) Because it has two triangles as bases, it has six vertices.D) All the angles formed by the edges are congruent.

Answer: C

Example 15.2 – Use properties to describe three-dimensional shapes:

Below are descriptions of some top, front, and side views of three-dimensional shapes. For each description identify a three-dimensional shape whose views match the given description, and sketch a view of it that shows its principle features.

a) Side and front views are triangles. Top view is a circle.b) Side and front views are rectangles. Top view is a circle.c) Side and front views are triangles. Top view is a square.d) Side and front view are rectangles. Top view is a rectangle.e) Side, top, and front views are all congruent squares.f) Side, top, and front views are all congruent triangles.

Source: Foundations of Success, Achieve, Inc. 2002

Answers:

a) Cone b) Cylinder

c) Square pyramid d) Rectangular prism

e) Cube f) Triangular pyramid

A shape is considered three dimensional if it can be measured in 3 directions.

 Three dimensional shapes can be measured in height, width, and depth.

 

Three Dimensional Shapes

 

 

Example

       Is this shape a three dimensional shape? 

Yes, this shape is a three dimensional shape because it can be measured in 3 directions.

A cylinder can be measured in height, width, and depth.

 

Remember:  Three dimensional shapes can be measured in height, width, and depth.