Building Blocks of Geometry

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Building Blocks of Geometry

Part I

Points, Lines and Planes The most basic figures of geometry

Point - an exact location. A

point A

It has no size at all, but is usually represented as a dot. Use a capital letter to name a point

Line - a straight path that extends without end in opposite directions. X

n

Y

Use two points on the line or a lowercase letter to name a line

Plane - a perfectly flat surface that extends infinitely in all directions Use three points in any order, not on the same line, to name a plane plane ABC

Identifying Points, Lines and Planes

Identifying Points, Lines and Planes

Identifying Points, Lines and Planes

Line Segments and Rays ray - a part of a line.

It has one endpoint and extends without end in one direction. Name the endpoint first when naming a ray.

Line segment- a part of a line or a ray that extends from one endpoint to another Use the endpoints in any order to name a line segment

Naming geometric figures

Congruent- figures that have the same shape and size Line segments are congruent if they have the same length. Use tick marks to indicate congruent line segments.

Guided Practice https://drive.google.com/open?id=0B38vJgVzMYKNakZsWnFIeXl0YXc

Individual Practice p. 444 1-12

https://www.ixl.com/math/grade-7 X.1Lines, line segments, and rays

Part II

Classifying Angles

angle • a figure formed by two rays that have the same initial point (The shared initial point is called the vertex.)

degrees •units used to measure angles (fraction of a circle)

CLASSIFICATIONS OF ANGLES

ACUTE •measures o between 0 o and 90

RIGHT •measures EXACTLY o 90

OBTUSE •measures o between 90 o and 180

STRAIGHT •measures EXACTLY 180

o

NAMING ANGLES

#1 BY THE VERTEX C A

1

T

∠ A

#2 BY A NUMBER ( NOT the measure ) C A

1

T

∠ 1

#3 BY 3 POINTS (vertex and 1 point on each ray)

C A

1

∠CAT or ∠TAC ***Order can be

T

reversed BUT the vertex MUST be in the middle!!!

Complementary Angles/Supplementary Angles If the sum of the measures of two angles is 90 degrees, then the angles are complementary angles. If the sum of the measures of two angles is 180 degrees, then the angles are supplementary angles.

Complementary Angles ✱ The sum of the measures of two complementary angles is

90°. < K and < M are complementary angles < K + < M = 90° Κ

Μ

Supplementary Angles ✱

The sum of the measures of two supplementary angles is 180°. < A and < B are Supplementary Angles < A + < B = 180°

Α

* A straight line = 180°

Β

Guided Practice https://drive.google.com/open?id=0B38vJgVzMYKNL Wg3SHl3dExTTnc

Independent Practice P. 450 1-21

Part III

Angle Relationships

PARALLEL LINES

*Always same distance apart, and never intersect!

PERPENDICULAR LINES

*Lines that intersect with each other to form 4 Right Angles (90°), often looks like the letter t , T

Intersecting Lines *Lines that intersect with each other through a common point *Lines that intersect form 4 angles, none of which are Right angles

IXL Practice X.2Parallel, perpendicular, intersecting

Skew Lines - do not intersect and they are not parallel. They lie in different planes.

Adjacent Angles -

Have a common vertex and a common side, but no common interior points Formed by two intersecting lines are supplementary

Vertical Angles ✱ When two lines intersect, two pairs of vertical angles

are formed. Vertical angles often look like the letter X.

Vertical angles < a and < b < c and < d
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