WARM UP

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WARM UP
Make a list of things you can and cannot assume
from the diagram.
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1.4 Beginning Proofs
Two-column Proofs and Theorems
Theorem a mathematical statement that can be
proven. PostulateMathematical statement accepted
as true.
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Theorem Procedures to follow

• We present a theorem or theorems
• We prove the theorem(s) using postulates
  definitions and other theorems.
• We shall omit the proofs of certain theorems,
  even though all have proofs

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Theorem Procedures to follow
3. We use the theorems to help prove sample
problems. 4.You are then given the challenge of
using the theorems to prove homework problems.
Theorems will save you much time if you learn
them and then use them!
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Theorem 1
If two angles are right angles, then they are
congruent.
Given ltA is a right angle ltB is a right
angle Prove ltA is congruent to ltB
A
B
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Theorem 1 - Proof
Statement Reason
1. ltA is right angle Given
2. mltA 90? If right angle then 90?
3. ltB is right angle Given
4. mltB 90? Same as 2
5. ltA congruent ltB If two angles have the same measure, then they are congruent. Steps 24
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Theorem 2
If two angles are straight angles, then they are
congruent.
Given ltABC is a straight angle ltDEF is a
straight angle Prove ltABC is congruent to ltDEF
B
C
A
E
F
D
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Theorem 2 - Proof
Statement Reason
ltABC is straight angle Given
2. mltABC 180 If angle is straight then m180
3. ltDEF is straight angle Given
4. mltDEF 180? Same as 2
5. ltABC congruent ltDEF If two angles have the same measure, then they are congruent. Steps 24