We may think of a point as a "dot" on a piece of paper.

We identify this point with a number or a CAPITAL letter.

A point has no length or width, it just specifies an exact location.

The term intersect is used when lines, rays, line segments or figures meet, that is, they share a common point.

IN THIS CASE THE POINT OF INTERSECTION IS D

STRAIGHT LINES don’t have a beginning or an end.

We usually name these lines with small letters like r,s,t…

r

We may think of a ray as a straight line that begins at a certain point and extends forever in one direction.

B

It has a beginning point and an endpoint

A

B

CURVED LINES

rr1

Two rays that share the same endpoint form an angle.

The point where the rays intersect is called the vertex of the angle.

The two rays are called the sides of the angle.

We usually specify an angle using Greek letters like these

We can also specify an angle with the letter of its vertex adding the symbol of angle like this A

AA

We measure the size of an angle using degrees.

ACUTE < 90º RIGHT= 90º OBTUSE > 90º

FLAT = 180º FULL= 360º

CLASIFICATION BYMEASUREMENT

Complementary Angles:

Two angles are called complementary angles if the sum of their degree measurements equals 90 degrees.

º

Supplementary Angles: Two angles are called supplementary angles if the sum of their degree measurements equals 180 degrees.

º

An angle bisector is a ray that divides an angle into two equal angles.

A polygon is a closed figure made by joining line segments, where each line segment intersects exactly two others.

The figure below is not a polygon, since it is not a closed figure:

The figure below is not a polygon, since it is not made of line segments:

The figure below is not a polygon, since its sides do not intersect in exactly two places each:

We’ve got two kinds of polygons:REGULAR AND IRREGULAR

examples of regular polygons examples of irregular

polygons

CONVEX POLYGONS: A figure is convex if every line segment drawn between any two points inside the figure lies entirely inside the figure.

THESE FUGURES ARE CONVEX

The following figures are concave. Note the red line segment drawn between two points inside the figure that also passes outside of the figure.

Note the red line segment drawn between two points inside the figure that also passes outside the figure.

The sum of the angles of a triangle is 180 degrees.

3 SIDES (TRIANGLES)

Equilateral TriangleA triangle that has three sides of equal length. The angles of an equilateral triangle all measure 60 degrees.

A triangle that has three sides of different lengths. So therefore, it has three different angles.

Acute Triangle : A triangle that has three acute angles.

Obtuse Triangle A triangle that has an obtuse angle.

One of the angles of the triangle measures more than 90 degrees.

Right TriangleA triangle that has a right angle. One of

the angles of the triangle measures 90 degrees.

A four-sided polygon. The sum of the angles of a quadrilateral is 360 degrees.

The radius of a circle is the distance from the center of the circle to the outside edge.

RADIUS

The diameter of a circle:

The diameter of a circle is the longest distance across a circle.  (The diameter cuts through the center of the circle.  This is what makes it the longest distance.)

(the perimeter of a circle)

The circumference of a circle is the perimeter -- the distance around the outer edge.

Circumference =

where r = the radius of the circleand pi = 3.141592...

A chord of a circle is a line segment that connects one point on the edge of the circle with another point on the circle.

(The diameter is a chord -- it's just the longest chord!)

An arc of a circle is a segment of the circumference of the circle.

A sector of a circle is a pie shaped portion of the area of the circle.

Technically, the piece of pie is between two segments coming out of the center of the circle.