Chapter Two Test Review
True (give reason) or False (give counterexample): The difference of any two numbers is a value that lies between those two numbers.
False; -8-(-5)=-3
True (give reason) or False (give counterexample): If angle A can be bisected, then angle A must be obtuse.
False; m<A=90 degrees
True (give reason) or False (give counterexample: The value of 2x is always greater than the value of x.
False; x=0
Write the converse of this statement: If a figure is a square, then it is a four-sided regular polygon.
If a figure is a four-sided regular polygon, then it is a square.
Write the if-then form of the statement: All squares are four-sided regular polygons.
If a figure is a square, then it is a four-sided regular polygon.
Write the contrapositive of this statement: If a figure is a square, then it is a four-sided regular polygon.
If a figure is not a four-sided regular polygon, then it is not a square.
Write the inverse of this statement: If a figure is a square, then it is a four-sided regular polygon.
If a figure is not a square, then it is not a four-sided regular polygon.
State the reason for the conjecture - Given: 2x-4=7; Conjecture 7=2x-4
Symmetric Property of Equality
What property is similar to the Law of Syllogism?
The Transitive Property
If you know that two angles are congruent, what can you say next in a proof?
Their measures are equal (Definition of Angle Congruence)
In a diagram, how can you tell if two angles are congruent?
They will have congruence markings.
State the reason for the conjecture - Given: AB=CD and CD=EF; Conjecture: AB=EF
Transitive Property of Equality
True (give reason) or False (give counterexample): If <A and <B are supplements and <B and <C are supplements, then <A and <C are congruent.
True; Congruent Supplements Theorem
True (give reason) or False (give counterexample): If m<JKL=m<GHI and m<GHI=m<ABC, then m<JKL=m<ABC.
True; Transitive Property of Equality
Can you assume from a diagram that two angles form a linear pair?
Yes!
Can you state that two line segments are perpendicular if there is a right angle marking at the intersection of the lines?
Yes!
Can you use a diagram to to state that two angles are vertical angles?
Yes!
If you know that the conditional statement "If a number is a rational number, then it is a real number," is true, and 4 is a rational number, what can you conclude and why?
4 is a real number; Law of Detachment
If you know that <A and <B form a linear pair, what can you say next in a proof?
<A and <B are supplementary (Linear Pair Postulate)
If you know that <A is supplementary to <B and <C is supplementary to <A, what can you say next in a proof?
<B is congruent to <C (Congruent Supplements Theorem)
When is a conjunction (^) false?
A conjunction is false unless both statements are true.
When is a disjunction (v) false?
A disjunction is only false if both statements are false. If one statement is true, then the disjunction is true.
State the reason for the conjecture - Given: <1 is supplementary to <2 and <3 is supplementary to <2; Conjecture: <1 is congruent to <3
Congruent Supplements Theorem
State the reason for the conjecture - Given: <RST is congruent to <PJG; Conjecture: m<RST=m<PJG
Definition of Angle Congruence
State the reason for the conjecture - Given: <7 is supplementary to <4; Conjecture: m<7+m<4=180 degrees
Definition of Supplementary Angles
State the reason for the conjecture - Given: m<7 + m<9 = 180 degrees; Conjecture: <7 is supplementary to <9
Definition of Supplementary Angles
State the reason for the conjecture - Given: <R is a right angle; Conjecture: m<R=90 degrees
Definition of a Right Angle
Write the contrapositive of the statement: If two lines intersect, then they form two pairs of vertical angles.
If two lines do not form two pairs of vertical angles, then they do not intersect.
Write the inverse of the statement: If two lines intersect, then they form two pairs of vertical angles.
If two lines do not intersect, then they do not form two pairs of vertical angles.
Write the converse of the statement: If two lines intersect, then they form two pairs of vertical angles.
If two lines form two pairs of vertical angles, then they intersect.
Write the if-then form of the statement: Two lines that intersect form two pairs of vertical angles.
If two lines intersect, then they form two pairs of vertical angles.
The following is an example of what Law of Logic: If you pass Geometry this year, you will take Algebra II next year. If you take Algebra II next year, you will learn more about functions. So, if you pass Geometry this year, you will learn more about functions.
Law of Syllogism
State the reason for the conjecture - Given: <1 and <2 form a linear pair; Conjecture: <1 is supplementary to <2
Linear Pair Congruence Theorem
Can you use a diagram to quantify the measure of an unmarked angle?
No!
Can you use a diagram to say that two lines intersect?
No!
If you know that the conditional statement "If the measures of two angles add up 180 degrees, then they are supplementary" is true and two angles are supplementary, can you make a valid conclusion using the Law of Detachment?
No! The hypothesis is not true, so we cannot use the Law of Detachment.
Can you assume from a diagram that two angles are complementary?
No! You can assume that the measure of the angle formed by the two angles is 90 degrees, then use the Angle Addition Postulate, the Transitive Property of Equality, and finally the Definition of Complementary Angles.
Can you assume from a diagram that two angles are supplementary?
No! You can assume they are a linear pair, and then use the Linear Pair Postulate to say they are supplementary.
State the reason for the conjecture - Given: Segment AB; Conjecture: Segment AB is congruent to Segment AB
Reflexive Property of Segment Congruence
State the reason for the conjecture - Given: <X and <Y are right angles; Conjecture: <X is congruent to <Y
Right Angle Congruence Theorem
State the reason for the conjecture - Given: Point S lies on line RT between R and T; RT=RS+ST
Segment Addition Postulate
If you know that m<1+m<2=90 degrees and m<3+m<4=90 degrees, what can you say next in a proof?
m<1+m<2=m<3+m<4 (Transitive Property of Equality)
