Show:
I know that property
Say what?
con - in - contra
Justify me!
Proof
100
Name the property that is used in the following example: 2(x+5)=2x+10
Distributive Property
100
True or False: The Law of Syllogism states that: if x --> y, and y --> z, then x --> z.
True
100
What is the biconditional of the following conditional statement? If a figure is a segment, then it has two endpoints.
A figure is a segment if and only if it has two endpoints
100
Justify the steps. 2x+5 + x -35 = 180 --> Given 3x - 30 = 180 --> ____________ 3x = 210 --> _______________ x = 70 --> __________________
simplify/combine like terms Addition property of equality (APE) Division Property of equality (DPE)
100
What always is listed in the first row of a 2-column proof?
The given statement
200
Name the property that is used in the following example: Angle 1=Angle 2 Angle 2=Angle 3 Therefore Angle 1=Angle 3
Transitive Property
200
Write the inverse of the following statment: If a quadrilateral has four equal sides and right angles, then it is a square.
If a quadrilateral doesnt have four equal sides and right angles, then it is not a square.
200
What is the converse of the given conditional statement? What is the truth value? If false, provide a counterexample. If x = 1, then x > 0.
If x > 0, then x = 1. False, if x = any positive number greater than 0.
200
Identify the properties. 3x + 1 = 10x - 20 1 = 7x - 20 --> _______________ 21 = 7x --> _______________ 3 = x --> _______________ x = 3 --> _______________
Subtraction property of equality Addition property of equality Division property of equality Symmetric property of equality
200
True or False: A conjecture is always true.
False
300
Name the property that demonstrates the following: Angle B=Angle B
Reflexive Property
300
Write the contrapositive of the following statement: If 2 angles are vertical, then they are congruent.
If two angles are not congruent, then they are not vertical.
300
What is the inverse of the given statement? If I graduate from high school, then I earn a high school diploma.
If I do not graduate from high school, then I do not earn a high school diploma.
300
Identify the property. If segment XY ≅ segment TZ and segment TZ ≅ segment AB, then segment XY ≅ segment AB.
transitive property of congruence
300
If the following step is listed in a 2-column proof, what would the reason be for the second line? 3x+4x+5=10 7x+5=10
Simplify
400
Name the property that is demonstrated by the following: 24x+12+6x+10=30x+22
Simplification or combining like terms
400
Determine the truth value for the below statement. If false, provide a counter example. If two angles are supplementary, then they cannot be congruent.
When the angles are both 90 degrees.
400
Identify the conditional and the converse of the given biconditional statement. A cat is happy iff it is purring.
Conditional: If a cat is happy, then it is purring. Converse: If a cat is purring, then it is happy.
400
∠1 and ∠2 are complementary. m∠1=4x-1 and m∠2=7x-8. Find the m∠2. Justify your steps
m∠1 + m∠2 = 90 --> Definition of complementary angles. 4x-1 + 7x-8 = 90 --> Substitution Property of Equality 11x - 9 = 90 --> simplify 11x = 99 --> Addition Property of Equality x = 9 --> Division property of equality m∠2=7x-8 m∠2=7(9) - 8 m∠2=63 - 8 m∠2= 55 degrees
400
If the following step is listed, what would the reason be? And what would your next step most likely be? AB + BC = AC
Segment Addition Postulate Substitution Property
500
Name the property that is demonstrated by the following: 2x=8 and x=4 2(4)=8
Substitution
500
Write the biconditional statement for the following conditional statement: If Chuck earns an A, he studied for his math test.
Chuck earns an A if and only if he studied for his math test.
500
What is the contrapositive of the following conditional statement? If a triangle is a right triangle, then it has exactly one right angle.
If a triangle does not have exactly one right angle, then it is not a right triangle.
500
225 + x = 225 + x
Reflexive property of equality
500
When considering justifications, "values/numbers" require properties of equality; Shapes/figures/segments require properties of ___________.
Congruence