Geometry Fall Final Review
Kaufman
Geometry
2013
Chapter 1 Topics
• We covered 4 sections in Chapter 1
– 1-1: Understanding Points, Lines, & Planes
– 1-2: Measuring and Constructing Segments
– 1-3: Measuring and Constructing Angles
– 1-4: Pairs of Angles
Let’s take a look at each section more closely…
Section 1-1: Understanding Points,
Lines, and Planes
• Undefined Terms in Geometry: point, line,
plane
• Collinear vs. Non-Collinear
• Coplanar vs. Non-Coplanar
• Segment
• Endpoint
• Ray
• Opposite Rays
Section 1-1 Continued
• Postulates
– Through any two points there is exactly one line
– Through any three noncollinear points there is
exactly one plane containing them
– If two points lie in a plane, then the line
containing those points lies in the plane
– If two lines intersect, then they intersect in exactly
one point
– If two planes intersect, then they intersect in
exactly one line
Section 1-2: Measuring and
Constructing Segments
• Congruent Segments: segments that have the
same length, marked with “tick marks”
• Between: If B is between points A and C, does
it have to be in the middle?
• Segment Addition Postulate: Part + Part =
Whole
• Midpoint
• Bisects
Section 1-3: Measuring and
Constructing Angles
• Angle: a figure formed by 2 rays (sides), with a
common endpoint (vertex)
• Interior and Exterior of angle
• Naming Angles
• Classifying Angles
– Acute
– Right
– Obtuse
– Straight
Section 1-3 Continued
• Congruent Angles: angles that have the same
degree measure. They are noted with arc
marks
• Angle Addition Postulate: Part + Part = Whole
• Angle Bisector: a ray that cuts an angle
directly in half
Section 1-4: Pairs of Angles
• Adjacent Angles: angles that share a side and
a vertex (next to each other)
• Linear Pair: two adjacent angles who form a
line and add up to 180 degrees
• Complementary Angles: two angles that add
up to 90 degrees (adjacent?)
• Supplementary Angles: two angles that add up
to 180 degrees (adjacent?)
• Vertical Angles: what is their relationship?
Section 2-1: Inductive Reasoning
• Inductive Reasoning: using examples and
patterns to determine if a statement is true or
false
• Conjecture: a statement you believe to be true
• Example: The product of an even number and
an odd number is…
• Counterexample: an example or case that
proves a conjecture to be false
Section 2-2: Conditional Statements
• Conditional Statement: If p, then q
• Hypothesis: the “p” part of the conditional
statement
• Conclusion: the “q” part of the conditional
statement
• Converse: If q, then p
• Inverse: If not p, then not q
• Contrapositive: If not q, then not p
Section 2-3: Deductive Reasoning
• Deductive Reasoning: using facts and
definitions to determine if a statement is true
• Proofs!
Section 3-1: Lines and Angles
(Note: no parallel lines given yet)
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Parallel Lines
Perpendicular Lines
Skew Lines
Parallel Planes
Transversal
Corresponding Angles
Alternate Interior/Exterior Angles
Same-Side Interior Angles
Section 3-2: Angles Formed by Parallel
Lines and Transversals
• Corresponding Angles Postulate: If lines are
parallel, then corresponding angles are…
• Alternate Interior Angles Theorem: If lines are
parallel, then alt. int. angles are…
• Alternate Exterior Angles Theorem: If lines are
parallel, then alt. ext. angles are…
• Same-Side Interior Angles Theorem: If lines
are parallel, then same-side interior angles
are…
Section 3-3: Proving Lines Parallel
• The converses of all the theorems/postulates
are also true
• For example, if you are not given that the lines
are parallel, you could show that
corresponding angles are congruent, and
therefore showing that the lines are parallel
by the Converse of the Corresponding Angles
Postulate
Section 3-4: Perpendicular Lines
• Perpendicular Bisector: A segment/line/ray
that is perpendicular to a segment at the
segment’s midpoint
• The shortest distance from a point to a line is
the perpendicular segment that would
connect the two. All other segments
connecting the point and line would be longer
than the perpendicular segment
Section 4-1: Triangles
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Acute Triangles
Obtuse Triangles
Right Triangles
Equiangualar Triangle
Equilateral Triangle
Isosceles Triangle
Scalene Triangle
Section 4-2: Triangles
• The sum of the angle measures of a triangle is
180 degrees.
• The acute angels of a right triangle are
complementary
• The measure of each angle of an equiangular
triangle is 60 degrees
• The measure of an exterior angle of a triangle
is equal to the sum of the measures of its
remote interior angles
Section 4-3: Triangles
• Congruent Polygons: all corresponding angles
and sides are congruent.
Section 4-4, 4-5: Triangles
• Triangle Congruence: SSS, SAS, ASA, AAS, HL
Section 4-6: Triangles
• CPCTC: Corresponding parts of congruent
triangles are congruent.
Section 4-8: Triangles
• If two sides of a triangle are congruent, then
the angles opposite the sides are congruent
• The converse is true
• If a triangle is equiangular then it is equilateral
Section 5-1: Perpendicular Bisector
• If a point is on the perpendicular bisector of a
segment, then it is equidistant from the
endpoints.
• The converse is True
Section 5-1: Angle Bisector
• If a point is on the bisector of an angle, then it
is equidistant from the sides of the angle.
• The converse is True
Section 5-4: Midsegment Thm
• A midsegment of a triangle is parallel to a side
of the triangle, and its length is half the length
of that side.
Section 5-5: Triangle Inequality
• The sum of any two side lengths of a triangle
is greater than the third side length
Section 5-7: Pythagorean Thm
• Right Triangle if, A^2 + B^2 = C^2
• Obtuse Triangle if, A^2 + B^2 < C^2
• Acute Triangle if, A^2 + B^2 > C^2
Section 5-8: Special Right Triangles
45-45-90 Triangle: both legs are congruent,
and the length of the hyp is the length of the
leg times ___
• 30-60-90 Triangle: the length of the hyp is 2
times the length of the shorter leg, and the
length of the longer leg is the length of the
shorter leg times ___