Conditionals
A conditional statement is written in a specific form.
What is "If-then" form.
Biconditional statement "key phrase".
"If and only if"
Deductive reasoning is also known as.
Logical reasoning
Name the property:
-2+x=15
x=17
Addition property
Name the theorem:
Vertical angles are congruent.
The hypothesis follows this part of a conditional statement.
What is the IF.
A biconditional statement is the combination of?
A conditional statement and its true converse.
The law of detachment states.
If a conditional is true, and its hypothesis is true, then its conclusion is true.
Name the property:
If a=b, then a-c =b-c.
Subtraction Property
What does the congruent supplements theorem state?
If two angles are supplements of the same angle or congruent angles, then the 2 angles are congruent.
The conclusion of this statement:
If an angle is a right angle, then its measure is 90 degrees.
What is its measure is 90 degrees.
The symbolic form of a biconditional with p and q.
p <--> q
The law of syllogism states.
If p --> q and q --> r are true statements,
then p --> r is a true statement.
Name the property:
5x=25
x=5
Division Property
What does the theorem about right angles state?
All right angles are congruent.
Write the statement in if-then form:
Vertical angles are congruent.
If two angles are vertical, then they are congruent.
Write the biconditional of these statements:
If two angles have the same measure, then the angles are congruent.
If two angles are congruent, then the angles have the same measure.
Two angles have the same measure if and only if the angles are congruent.
By the law of detachment we can conclude:
If angle A is acute, then the measure of angle A is less than 90 degrees.
Angle A is acute.
The measure of angle A is less than 90 degrees.
Name the property:
4=4
Reflexive Property
What are the measures of congruent adjacent supplementary angles.
90 and 90
The converse of a conditional is...
The hypothesis and conclusion switched.
Separate this biconditional into a conditional statement and a converse statement:
Three point are collinear if and only if they lie on the same line.
Conditional: If three points are collinear, then they lie on the same line.
Converse: If three pants like on the same line, then they are collinear.
Use the law of syllogism to draw a conclusion:
If a quadrilateral is a square, then it contains four right angles.
If a quadrilateral contains four right angles, then it is a rectangle.
If a quadrilateral is a square, then it is a rectangle.
Name the property:
If angle A is congruent to angle B, then angle B is congruent to Angle A.
Symmetric Property
What are the measure of congruent adjacent complementary angles?
45 and 45