If-Then
The hypothesis of the conditional statement:
"If two lines intersect, then vertical angles are created"
Two lines intersect
Assume all given information is true to make a conclusion:
If it's Tuesday, then Billy will be at the movies. It's Tuesday.
Billy will be at the movies
Assume all given information is true to make a conclusion:
If it's a cat, it will lie in the sun. If it lies in the sun, then it will purr.
If it's a cat, then it will purr.
The length of AB if X is the midpoint of segment AB and AX=14.
AB=28
Same size and same shape
Congruent
The conclusion of the conditional statement:
"If it is a square, then it has 4 congruent sides"
Assume all given information is true to make a conclusion:
If it's Tuesday, then Billy will be at the movies. Billy is at the movies.
No Logical Conclusion
Assume all given information is true to make a conclusion:
If it's Wednesday, then Laura must go to work. If Laura goes to work, then she'll ride the transit.
If it's Wednesday, then she'll ride the transit.
The measure of <A if <A and <B are supplementary, and m<B=120 degrees
m<A=60 degrees
A pair of adjacent angles (side by side) that take the shape of a line and add up to 180 degrees
Linear Pair
The truth value of the statement:
"If two angles form a linear pair, then they are supplementary"
TRUE
Assume all given information is true to make a conclusion:
When an angle is bisected, it creates 2 congruent angles. An angle is bisected.
2 Congruent Angles are created
Assume all given information is true to make a conclusion:
If you ride a bike, you are exercising. If you are exercising, your heart rate will increase.
If you ride a bike, your heart rate will increase.
The value of x when <1 and <2 are vertical angles and m<1=5x+21 and m<2=12x-7.
x=4
A pair of rays that share the same endpoint and extend in opposite directions, taking the shape of a line and creating a 180 degree angle.
Opposite Rays
The manner in which a conditional statement can be proven false
COUNTEREXAMPLE
Assume all given information is true to make a conclusion:
If a segment is bisected, then 2 congruent segments are created. 2 congruent segments are created.
No Logical Conclusion
Assume all given information is true to make a conclusion:
If you have french fries, then you'll have a full stomach. If you order a burger, you'll also have french fries.
If you order a burger, then you'll have a full stomach.
The value of y when <R and <T are a linear pair, and m<R=7y and m<T=5y.
y=15
A pair of angles, created when two lines intersect, that are directly across from each other.
Vertical Angles
The truth value of the biconditional:
"Two angles are a linear pair, if and only if, they are supplementary"
FALSE
Assume all given information is true to make a conclusion:
If 2 angles measures are equal, then they are congruent. Angle 1 and Angle 4 each measure 32 degrees.
Angle 1 and Angle 4 are Congruent
Assume all given information is true to make a conclusion:
If a dog is a cat, then a cat is a mouse. If a cat is a mouse, then a dog is a giraffe.
If a dog is a cat, then a dog is a giraffe.
The length of the line segment that has endpoints at (2,8) and (6,11).
5
A type of reasoning that reaches conclusions using given and previously known facts and/or definitions
Deductive Reasoning