Geometry Midterm '22
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46 Terms
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Congruent
identical in form
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Adjacent
share (a) a common side **and** (b) a common vertex
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Complementary Angles
combines to equal 90\*
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Supplementary Angles
combines to equal 180\*
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Linear pair
two adjacent angles that add up to 180\*, creates a line.
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obtuse
greater than 90 less than 180\*
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right
90\*
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acute
less than 90\*
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straight
angle measure = to 180\*
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parallel lines
same distance apart, don’t intersect, same slope
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perpendicular lines
intersect to form 90\*, (opposite and reciprocal slope, product of their slopes is -1)
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skew lines
dif slopes, dont intersect, exist on dif. planes
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coplanar
exist on the same plane
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collinear
exist on the same line
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Whats the hypothesis (p)?
\
If charlie has an A in the class, then he never failed a test.
\
If charlie has an A in the class, then he never failed a test.
If charlie has an A in the class
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What’s the conclusion?
\
If charlie has an A in the class, then he never failed a test.
\
If charlie has an A in the class, then he never failed a test.
then he never failed a test.
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Converse
q → p
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Inverse
\~p → \~q
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Contrapositive
\~q → \~p
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Inductive reasoning
specific observation → pattern recognition → general conclusion
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Deductive reasoning
existing theory → formulate hypothesis → collect data → analyze data → do/don’t reject hypothesis
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2-point postulate
**Through any two points there exists exactly one line.**
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Line-point postulate
a line contains at least 2 points
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Line intersection
if 2 lines intersect, then their intersection is exactly one point
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3-point
**Through any three noncollinear points, there exists exactly one plane.**
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Plane point
A plane contains at least three noncollinear points.
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plane line
If two points lie in a plane, then the line containing them lies in the plane.
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plane intersection
**If two planes intersect, then their intersection is a line.**
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parallel postulate
If there is a line and a point not on the line, then there is exactly one line through the point parallel to the given line.
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perpendicular postulate
**If there is a line and a point not on the line, then there is exactly one line through the point perpendicular to the given line.**
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addition property of equality
if a = b, then a + c = b + c.
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subtraction property of equality
if a = b, then a - c = b - c.
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multiplication property of equality
if a = b, then a x c = b x c.
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division property of equality
if a = b, then a / c = b / c.
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Substitution Property of Equality
if a = b, then a can be substituted for b (or b for a) in any equation or expression.
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Distributive property
sum: a(b + c) = ab + ac
difference a(b-c) = ab - ac
difference a(b-c) = ab - ac
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reflexive property
a = a; a number is always equal to itself
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symmetric property
if a = b, then b = a; values on either side of the equal sign are equal and will remain equal if the sides are flipped
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transitive property
If a = b and b = c, then a = c.
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corresponding angles:
1-5
2-6
4-8
3-7
2-6
4-8
3-7
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alternate interior angles:
4-5
3-6
3-6
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alternate exterior angles:
1-8
2-7
2-7
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consecutive interior angles:
4-6
3-5
3-5
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linear pairs:
1-2
2-4
4-3
3-1
5-6
6-8
8-7
7-5
2-4
4-3
3-1
5-6
6-8
8-7
7-5
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vertical angles:
1-4
2-3
5-8
6-7
2-3
5-8
6-7
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reflections:
y-axis
x-axis
y=m
y=-m
y-axis
x-axis
y=m
y=-m
1. (-x,y)
2. (x,-y)
3. (y,x)
4. (-y,-x)
Note 
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