Conditionals
State the CONVERSE of the following:
If you can play the piano, then you are talented.
If you are talented, then you can play the piano.
You are solving the following equation: x - 4 = 12. To solve for x, what property do you need to use?
Addition Property of Equality
This it the first reason listed in any proof.
Given
If a number is even, then it is divisible by 2.
If the converse is true, write the statement as a biconditional. If the converse is false, give a counter-example.
True
A number is even if and only if it is divisible by 2.
<ACE and <DCF are vertical angles. The m<ACE = 3x + 36. The m<DCF = 6x - 9. What are the measures of each angle?
81 degrees
If pigs had wings, then you could fly.
What is the hypothesis?
What is the conclusion?
Hypothesis: Pigs had wings.
Conclusion: You could fly.
In the equation 3(x -2) = 12, the first property used to solve for x will be this property.
Distributive Property
An obtuse angle has a measure more than 90 degrees.
Is this a good definition?
a) No, not accurate
b.) No, uses words not previously defined.
c.) No, contains too much information.
d.) Yes, it is a good definition.
A.) No, not accurate.
What are the two conditional statements that form this biconditional?
A quadrilateral is a trapezoid if and only if it has exactly one pair of parallel sides.
1.) If a quadrilateral is a trapezoid, then it has exactly one pair of parallel sides.
2.) If a quadrilateral has exactly one pair of parallel sides, then it is a trapezoid.
< A and < B are supplementary and < A and < C are supplementary. Based on this information, what conclusion can you reach?
< B and < C are congruent.
Give an instance to the conditional: If x<= 20, then x < 10.
A number less than 10.
If a = b, then b = a.
Symmetric Property
Name three things that can be used as reasons in proofs.
Given Information, Definitions, Postulates, Properties, Proven Theorems
A person who lives in Cleveland is a person who lives in Ohio.
Can this be written as a biconditional? Why or why not?
No, since the converse would not be true.
TE - Standardized Test Prep - diagram 4
Find the angle measures of all 4 angles
The angles with x are 130 degrees.
The angles with y are 50 degrees.
Give a counter-example to the conditional: If x<= 20, then x < 10.
A number greater than 10 but less than or equal to 20.
If <A is congruent to <B and <B is congruent to <C, then __________________.
Bonus: What property is this an example of?
<A is congruent to <C
Transitive Property of Congruence
A similarity transformation is a composition of a rigid motion and a dilation.
Is this a good definition?
a) No, not accurate
b.) No, uses words not previously defined.
c.) No, contains too much information.
d.) Yes, it is a good definition.
No, uses words not previously defined.
When can a conditional be written as a biconditional?
When both the conditional and its converse are true.
<A and <B are complementary angles. If m<A = 5x - 2 and the m<B = 3x + 4, then what are the angle measures?
m<A = 53
m<B = 37