U1 Definitions
Two segments are congruent if and only if ...
... their lengths are equal.
True or false?
If a number is a multiple of 10, then it is even.
True
The floor is not lava.
Write the segment addition postulate.
If B is between A and C, then AB + BC = AC.
What are the headings for each column in a two-column proof?
If a point is a midpoint of a segment, then ...
... it divides the segment into two congruent segments.
Write the statement that follows from these two:
1. x is a negative number.
2. If x is negative, then x2 is positive.
x2 is positive
Original statement: If the sun is shining, then it is daytime
??: If it is daytime, then the sun is shining.
Converse statement
Which property is this?
If a = b, then a + c = b + c
Addition Property of Equality
What type of proof uses boxes and arrows to show a logical argument?
Flowchart proof
If two angles are both supplementary and adjacent, then ...
... they form a linear pair.
Write the statement that follows from these two:
1. If a figure is a rhombus, then the figure is a parallelogram.
2. If a figure is a parallelogram, then the figure has two pairs of opposite sides that are parallel.
If a figure is a rhombus, then the figure has two pairs of opposite sides that are parallel.
Original statement: If the sun is shining, then it is daytime
Write the contrapositive.
If it is not daytime, then the sun is not shining.
Which property is this?
If a = b and b = c, then a = c.
Transitive Property of Equality
What are allowed in the "reasons" column of a two column proof?
Definitions, properties, postulates, and proven theorems
If the measures of two angles sum to 90º, then ...
... the angles are complementary.
A line s divides segment MN into two line segments, so line s is a segment bisector of MN.
[Answers may vary]
Some drawing with line s intersecting anywhere but the midpoint.
Which two pairs of statements are equivalent?
original and contrapositive;
converse and inverse
Write the angle addition postulate.
If R is in the interior of ∠PST, then m∠PSR + m∠RST = m∠PST.
Given: AC = BD
Prove: Segment AC is congruent to Segment BD.
What definition(s), property(s), or postulate(s) would be used in this (short) proof?
The definition of congruence
If two angles are supplementary, then ...
... their angle measures sum to 180º.
What conclusion can you make from these statements?
1. If a figure is a square, then it has four right angles.
2. If a figure is a square, then it has four congruent sides.
No conclusion can be made.
In addition to the original conditional statement being true, ______ needs to be true for a biconditional statement to be true.
the converse statement.
What property is used to say that if 3x + 5y = 7, and y = 2x + 4, then 3x + 5(2x + 4) = 7?
Substitution Property of Equality
Given: ∠ABC and ∠DEF are congruent, m∠ABC = 48º.
Prove: m∠DEF = 48º
What definition(s), property(s), or postulate(s) would be used in this proof?
Definition of congruence and the transitive property