Geometry Midterm '22

Congruent

identical in form

Adjacent

share (a) a common side and (b) a common vertex

Complementary Angles

combines to equal 90*

Supplementary Angles

combines to equal 180*

Linear pair

two adjacent angles that add up to 180*, creates a line.

obtuse

greater than 90 less than 180*

right

90*

acute

less than 90*

straight

angle measure = to 180*

parallel lines

same distance apart, don’t intersect, same slope

perpendicular lines

intersect to form 90*, (opposite and reciprocal slope, product of their slopes is -1)

skew lines

dif slopes, dont intersect, exist on dif. planes

coplanar

exist on the same plane

collinear

exist on the same line

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

What’s the conclusion?

If charlie has an A in the class, then he never failed a test.

then he never failed a test.

Converse

q → p

Inverse

~p → ~q

Contrapositive

~q → ~p

Inductive reasoning

specific observation → pattern recognition → general conclusion

Deductive reasoning

existing theory → formulate hypothesis → collect data → analyze data → do/don’t reject hypothesis

2-point postulate

Through any two points there exists exactly one line.

Line-point postulate

a line contains at least 2 points

Line intersection

if 2 lines intersect, then their intersection is exactly one point

3-point

Through any three noncollinear points, there exists exactly one plane.

Plane point

A plane contains at least three noncollinear points.

plane line

If two points lie in a plane, then the line containing them lies in the plane.

plane intersection

If two planes intersect, then their intersection is a line.

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.

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.

addition property of equality

if a = b, then a + c = b + c.

subtraction property of equality

if a = b, then a - c = b - c.

multiplication property of equality

if a = b, then a x c = b x c.

division property of equality

if a = b, then a / c = b / c.

Substitution Property of Equality

if a = b, then a can be substituted for b (or b for a) in any equation or expression.

Distributive property

sum: a(b + c) = ab + ac

difference a(b-c) = ab - ac

reflexive property

a = a; a number is always equal to itself

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

transitive property

If a = b and b = c, then a = c.

corresponding angles:

1-5

2-6

4-8

3-7

alternate interior angles:

4-5

3-6

alternate exterior angles:

1-8

2-7

consecutive interior angles:

4-6

3-5

linear pairs:

1-2

2-4

4-3

3-1

5-6

6-8

8-7

7-5

vertical angles:

1-4

2-3

5-8

6-7

reflections:

y-axis

x-axis

y=m

y=-m

1. (-x,y)

2. (x,-y)

3. (y,x)

4. (-y,-x)