1-3 Points, Lines, Planes

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1st Semester Geometry Notes page 1
1-3 Points, Lines, Planes
plane M or plane ABC (name with 3 pts)
A
point A
Points A, B, and C are coplanar
Points A, B are collinear

• Intersection of two distinct lines is a point
• Intersection of two distinct planes is a line

1-4 Segments, Rays, Parallel Lines, Planes
Parallel Lines -Never intersect -Extend in the
same directions -Coplanar
Segment AB or

• Opposite rays share same endpoint
• Opposite rays are collinear

Skew Lines -Never intersect -Extend in different
directions -Noncoplanar
Parallel Planes -Can never intersect
1-5 Measuring Segments
AB is the abbreviation for the distance between
points A and B.
Segment Addition Postulate

• Midpoint
• B is exactly halfway between A and C
• B is the average coordinate of A and C

1-6 Measuring Angles
vertex
Congruent Angles m? 1 m? 2 (the measure of
angle 1 equals the measure of angle 2) ? 1 ? ? 2
(Angle 1 is congruent to angle 2) (May also be
indicated by arc on both angles)
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1st Semester Geometry Notes page 2
Pairs of Angles
?1 and ?2 are adjacent angles -No interior
points in common
-Share the same vertex R
-Share common side
Vertical Angles -Non-adjacent -Formed by two
intersecting lines -Are congruent
Angle Addition Postulate
m?AOB m?BOC m?AOC
?1 and ?3
?2 and ?4
Linear Pairs -Form a straight angle -Are
supplementary (sum 180)
Compl. Corner
Suppl. Straight
2-1 2-2 2-3 5-4 Deductive Reasoning
1-1 Inductive Reasoning
Conditional If a, then b statement a is the
hypothesis b is the conclusion Converse
Switch the hypothesis and conclusion. If b, then
a. Truth value of a statement Either True or
False, where True means always true Biconditional
Both the conditional and its converse are true.
You can combine both statements with if and only
if. a if and only if b.
Law of Detachment If a, then b. (True) Given
a is True b is therefore True.
Law of Syllogism If a, then b. (True) If b,
then c. (True) If a, then c must be True.
2-4 Algebraic Properties
If A is falls to the right, then B falls to the
right
A B C
A B
If B is falls to the right, then C falls to the
right. If A falls to the right, then C falls to
the right.
Given A falls to the right is True Then B
falls to the right.
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1st Semester Geometry Notes page 3
1-8 8-1 Pythagorean Theorem, Midpoint, Distance
Formula
Pythagorean Theorem
Classifying Triangles
Let a, b, c be the lengths of the sides of a
triangle, where c is the longest Acute c2 lt a2
b2 Right c2 a2 b2 Obtuse c2 gt a2 b2
(leg1)2 (leg2)2 hypotenuse2 True only for
right triangles
Distance between 2 points -Use the Pythag. Thm
Midpoint (average x, average y)
3-1 3-2 3-3 Parallel Lines and Angles
Transversal line that cuts across two or more
lines
Same-side exterior
?1 and ?4 ?5 and ?8
Congruent if and only if l and m are parallel
Vertical angles are congruent Linear pairs are
supplementary
Supplementary if and only if l and m are parallel
3-4 Triangle Sum Thm, Exterior Angle Thm
4-5 Isosceles and Equilateral Triangles
A triangle is isosceles if and only if the base
angles are congruent. A triangle is equilateral
if and only if the triangle is equiangular
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1st Semester Geometry Notes page 4
3-5 Polygon Angle Sum Thms n number of sides
Interior angle
Exterior angle
180
for regular polygons
3-6 3-7 Graphing Equations of Lines

• Any point on the line must satisfy the equation
  of the line (y mx b)
• Parallel lines have equal slopes (same steepness)
• Perpendicular lines have slopes
• that are negative reciprocals of each other

Standard Form Ax By C Point-Slope Form y
y1 m (x x1)
9-2 Reflections Preimage and image are -on
opposite sides of line of reflect. -equidistant
from line of reflection Reflect about x-axis (x,
y) ? (x, -y) Reflect about y-axis (x, y) ? (-x,
y) Reflect about y x (x, y) ? (y, x)
9-1 Translations (x, y) ? (xa, yb)
9-3 Rotations about origin For each 90 of
rotation, switch the x and y coordinates then
determine signs based on the quadrant after
rotation
Preimage before the transformation Image after
the transformation Isometry size and shape stay
the same Reflections, Translations, and Rotations
are isometries
9-5 Dilations
9-4 Symmetry
Enlargement Multiply both x and y by a scale
factor k greater than 1 (x, y) ? (kx,
ky) Reduction Multiply both x and y by a scale
factor k between 0 and 1 (x, y) ? (kx,
ky) Vertical stretch Multiply the y only by a
scale factor k greater than 1 (x, y) ? (x, ky)
Horizontal shrinkage Multiply the x only by a
scale factor k between 0 and 1 (x, y) ? (kx, y)
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1st Semester Geometry Notes page 5
7-1 Ratios and Proportions
7-2 Similarity

7-3 Proving Triangles Similarity SSS, SAS, AA
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1st Semester Geometry Notes page 6
7-4 Similarity in Right Triangles

• Redraw and label triangles.
• Fill in the table with given information
• Use proportions or Pythag. Thm to solve for
  missing lengths

7-5 Proportions in Triangles
in a triangle
4-1 Congruent Polygons
Two polygons are congruent if they have the same
size and shape. Two polygons are congruent if
and only if all corresponding sides and
corresponding angles are congruent.
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1st Semester Geometry Notes page 7
4-2 4-3 4-6 Proving Triangles Congruent SSS SAS
ASA AAS HL
4-4 4-7 Using CPCTC in Proofs
CPCTC is an abbreviation of the phrase
Corresponding Parts of Congruent Triangles are
Congruent.
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1st Semester Geometry Notes page 8
5-5 Triangle Inequalities
Given two sides a and b, the third side the
triangle with length c must satisfy a b lt c
lt a b
5-1 5-2 5-3 Special Segments in Triangles
Altitudes (vertex to opposite side at right
angles Orthocenter Perpendicular
Bisectors (90 degrees through midpoint of a side)
Circumcenter Medians (vertex to midpoint
of opposite side) Centroid
Angle Bisectors (vertex to opposite side through
line splitting the vertex angle in half Incenter