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Planning a Proof
Lesson 2.6
Geometry Honors
Page 60
Objective:
Lesson Focus
Before a proof is written, a plan should be developed.
A plan is a method that can be tried to write a proof.
If the plan does not work, a new plan should be developed
and tried.
Planning a Proof
Right Angle Congruence Theorem
All right angles are congruent.
Congruent Complements Theorem
If two angles are complements of congruent angles (or of the
same angle), then the two angles are congruent.
Congruent Supplements Theorem
If two angles are supplements of congruent angles (or of the
same angle), then the two angles are congruent.
Linear Pair Postulate
If two angles form a linear pair, then they are supplementary.
Planning a Proof
• You may feel more comfortable writing detailed proofs at first.
With experience, you will be able to omit the minor steps in a
proof, though in the beginning it may be better to err on the
side of more detail.
• Write proofs that you think are logically sound. Develop a
chain of if-then statements.
• Try to explain your proof orally to a friend to see if they can
follow your reasoning.
Planning a Proof
Parts of a Proof:
1.
2.
3.
4.
5.
Statement of the theorem.
A diagram that illustrates the given information.
A list, in terms of the figure, of what is given.
A list, in terms of the figure, of what you are to prove.
A series of statements and reasons that lead from the given
information to the statement that is to be proved.
Planning a Proof
When writing a reason for a step in a proof, you must use one
of the following
• Given information
• A definition
• A property
• A postulate
• A previously proven theorem.
Planning a Proof
Given: 2 and 3 are supplementary.
Prove: m1 = m3
Plan:
1
2
3
4
Planning a Proof
Given: 2 and 3 are supplementary.
Prove: m1 = m3
Plan: 2 is supplementary to 1;
2 is supplementary to 3;
therefore 1  3.
1
2
3
4
Planning a Proof
Given: 2 and 3 are supplementary.
Prove: m1 = m3
Plan: 2 is supplementary to 1;
2 is supplementary to 3;
therefore 1  3.
Proof:
Statement
1
2
3
4
Reason
1. 2 is supplementary to 1
1. Definition of Supplementary Angles
2. 2 is supplementary to 3
2. Given
3. 1  3
3. If two angles are supplements of
congruent angles (or the same angle),
then the two angles are congruent.
4. m1 = m3
4. Definition of Congruent Angles
Planning a Proof
Given: m1 = 4.
Prove: 4 is supplementary to 2
Plan:
1
2
3
4
Planning a Proof
Given: m1 = 4.
Prove: 4 is supplementary to 2
1
Plan: m1 = m4;
1 is supplementary to 2;
therefore 4 is supplementary to 2.
Proof: (Writing the proof is left to the student.)
2
3
4
Homework
Pages 63 – 65/68 - 69
Problems:
15 – 25 odd
Chapter Test