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geo quiz chpt 2.1 2.4
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Terms in this set (19)
Inductive Reasoning
find the pattern and make a conjecture
conditional
p-> q if p then q
If a polygon has 8 sides, then it is an octagon
example of conditional
An angle that measures 45 degrees is an acute angle
if an angle measures 45 degrees, then it is an acute angle.
Converse
if q then p goes with inverse
inverse
if not p then not q ( USE ~ for not) take original statement add not goes with converse
contrapositive
if not q then not p so take original statement turn it around and add not goes with the conditional statement
In Miguels town, the month of April has had the most rain for the past 5 years. He thinks that April will have the most rain this year.
Inductive
he found a pattern
Sandra learned that if it is cloudy at night it will not be as cold in the morning than if there are no clouds at night. Sandra knows it will be cloudy tonight. so she believes it will not be cold tomorrow.
Deductive
law of detachment if p then q is true and p is true then q is true
an example
If a car is out of gas, then it will not start.
Sarahs car is out of gas
valid conclusion: sarahs car will not start
If a ray divides an angle into two congruent angles, then the ray is an angle bisector.
RS divides angle ARB so that angles ARS is congruent to angle SRB
valid conclusion RS is an angle bisector
If two angles are adjacent, then they share a common vertex.
Angle 1 and 2 share a common vertex.
NO VALIDITY
angle 1 and 2 could share a vertex being vertical lines and not be adjacent
If a triangle is a right triangle, then the triangle has one 90 degree angle.
triangle ABC is a right triangle
triangle ABC has one 90 degree angle
If a parallelogram has four congruent sides, then the parallelogram is a rhombus.
The parallelogram has four congruent sides.
The parallelogram is a rhombus
Law of syllogism
if then plus another if then
If you get a job, then you will earn money,
I you earn money, then you will buy a car.
If you get a job, you will buy a car.
If a figure is a square, then the figure is a rectangle.
If a figure is a rectangle. then the figure has four sides.
If a figure is a square, the the figure has four sides.
If a number is divisible by 12, then it its divisible by 6.
If a number is divided by 6, then it is divisible by three.
If a number is divisible by 12 then the figure is divisible by three.
If you take calculus, you must take Alg 2 .
To take alg 2, you must take Alg 1
If you take Calculus you must take Alg 1.
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