Page 190 - Math Course 2 (Book 2)

Postulates and Paragraph Proofs

MO. 12 - L5b paragraph proof
A paragraph to explain why a conjecture for a
Paragraph Proofs Using given situation is true.

Postulates informal proof

A paragraph to explain why a conjecture for a given
situation is true.
Vocabulary A-Z

Let us learn some vocabulary Given: M is the midpoint of PQ
Prove: PM ≅ MQ

theorem From the definition of midpoint of a segment,
Once a statement or conjecture has been shown to PM = MQ. This means that PM and MQ have the
be true, it is called a theorem. same measure. By the definition of congruence, if

two segments have the same measure, then they
Pythagorean Theorem c = 25
2
2
a + b = c 2 are congruent. Thus, PM ≅ MQ.
2
16 + 9 = 25 Q
C M
A Right P

Angle
Triangle THEOREM 12.1
B b = 9 Midpoint Theorem
2
a = 16
2

If M is the midpoint of AB, then AM ≅ MB.
proof
a logical argument in which each statement you
make is supported by a statement (a theorem or Key Concept
postulate) that is accepted as true.

C Five essential parts of a good proof:
B
A • State the theorem or conjecture to be proven.
D Given: • List the given information.
E FE = BC • If possible, draw a diagram to illustrate the given
F AB || ED AF || CD information.
• State what is to be proved.
Statement Reason • Develop a system of deductive reasoning.

1. AB || ED given

2. AF || CD given

alternate interior angles of
3. ∠ABF = ∠CED
parallel lines are congruent
4. FE = BC given

alternate interior angles of
5. ∠AFB = ∠DCE
parallel lines are congruent.
6. △ABF ≅ DCE AAS Postulate

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