Download Chapter 1 – Basics of Geometry 1.2 Points, Lines, and Planes

Chapter 1 – Basics of Geometry
1.2 Points, Lines, and Planes
Symbols in Geometry:
line UT
line segment RY
ray AB
Opposite Rays:
-two rays that share an ____________ point and extend in complete ________________directions
picture:
Conclusions from Vocabulary:
Two planes intersect at one ______________.
Two lines intersect at one _______________.
Naming Collinear and Coplanar Points:
Name three collinear points.
Name four points that are coplanar.
Name three points that are not collinear.
Drawing Lines, Segments, and Rays:
Draw three noncollinear points, J, K, and L.
Then draw JK , KL , and LJ .
Sketching Intersections:
Sketch a line that intersects a plane in one point.
Draw two planes that intersect in a line.
Chapter 1 – Basics of Geometry
1.3 Segments and Their Measures
Finding the Distance Between Two Points
Measure the line segment in centimeters. (be exact)
Measure the line segment in inches. (be exact)
Using the Segment Addition Postulate
If AB = 2 and AC = 9, how long is BC? ______________
(figure not drawn to scale)
If AB = 2x-6, BC = -4x+100, CD = x+7, and AD = 93, what is the value of x? __________________
1.3 and 1.5 Distance and Midpoint
Using the Distance Formula
What is the distance between (-2, 4) and (9, 8)?
Chapter 1 – Basics of Geometry
Distance Formula Shortcut (Pythagorean Theorem)
What is the distance between (-2, 4) and (9, 8)?
What is the distance between (1, 3) and (-10, -4)?
Using the Midpoint Formula
What is the midpoint of (-2, 3) and (5, -2)?
The midpoint of line segment RP is M(2, 4). One endpoint is R(-1, 7). Find the coordinates of endpoint
P.
Chapter 1 – Basics of Geometry
Midpoint Formula Shortcut (Average)
You can find the midpoint of a segment by finding the _______________ of the x-values and the
______________ of the y-values.
Use that fact to quickly find the midpoint of (0, 6) and (-4, 12).
1.4 Angles and Their Measures
Parts of an Angle
Label the vertex and sides of the angle at the right.
Three ways to name this angle:
Naming Angles
What is the other name for
COB?
What is the other name for
BOA?
What is the other name for
COA?
YOU CANNOT USE __________ TO NAME ANY OF THE ANGLES SHOWN ABOVE.
WHY?
Measuring Angles
You use a ____________ to measure a line segment and a _______________ to measure an angle.
Line segments may be measured in _____________, ______________, _____________, etc. but an
angle can only be measured in _________________.
Chapter 1 – Basics of Geometry
If two angles have the same measure, then they are __________________________.
picture and notation:
When I use a protractor, I must use my ______________ to determine which number to read as the
angle measure.
Since this angle is ________ than 90o, then I know I
would read the angle measure as _________,
NOT __________.
Since this angle is __________ than 90o, then I know I
would read the angle measure as _________,
NOT _________.
Using the Angle Addition Postulate
If m PQS = 35 and m PQR = 72, what is the m SQR?
If
ADC = (6x+8)o, find the angle measures for the three angles in the picture.
ADB ___________
BDC ___________
ADC ___________
Chapter 1 – Basics of Geometry
1.6 Angle Pair Relationships
Key Concepts
Vertical angles are ______________.
The sum of the measures of angles that form a linear pair is _______ because a line measures ________.
Finding Angle Measures
Name the 2 sets of vertical angles:
Name the 4 sets of linear pairs:
If m 2 = 130, find the measure of the other 3 angles in the picture above.
m 1 = _______________
m 3 = _______________
m 4 = _______________
In the picture at the right:
m AEB = (3x+5)o
m BEC = (y+20)o
m CED = (4y -15)o
m DEA = (x+15)o
Solve for x, then find the measure of each of the 4 angles mentioned.
(Before you start, let’s think…I can only solve for one variable at the time. If I choose to solve for x first, I
am given expressions for
_____ and
_____ that both involve x. These two angles are ____________
_____________. That means, if I add them together, then they should equal ______o. OK, now set up
your problem and solve it.)
Chapter 1 – Basics of Geometry
Complementary and Supplementary Angles
Complementary angles must be a set of _______ angles. They can be __________ or _______________.
adjacent complementary angles:
nonadjacent complementary angles:
Supplementary angles must be a set of _______ angles. They can be __________ or _______________.
adjacent supplementary angles:
nonadjacent supplementary angles:
MY way to remember the difference between complementary and supplementary angles