Download (a) Write a justification for each step, given that

CP Geometry
2.6 – Geometric Proofs
Name: ___________
Date: _____ Block: ____
It is important to justify each logical step with a reason. You can use ____________ and
___________________, but they must be clear enough so that anyone who reads your proof will
understand them.
Example1:
(a) Write a justification for each step, given that <A and <B are supplementary and m<A =
45°.
1.
A and B are supplementary.
m A = 45
2. m A + m B = 180
3. 45 + m B = 180
4. m B = 135
(b) Write a justification for each step, given that B is the midpoint of AC and AB
1.
2.
3.
4.
EF.
B is the midpoint of AC.
AB BC
AB EF
BC EF
A theorem is __________________________________________________
_____________________________________________________________________________.
Linear Pair Theorem:_______________________________________________________
_____________________________________________________________________________.
Hypothesis:
Conclusion:
Congruent Supplements Theorem: _________________________________________________
______________________________________________________________________________
_____________________________________________________________________________.
Hypothesis:
Conclusion:
A geometric proof begins with Given and Prove statements, which restate the hypothesis and
conclusion of the conjecture.
In a two-column proof, you list the steps of the proof in the ______________. You write the
matching reason for each step in the _______________________.
Example 2: Fill in the blanks to complete the two-column proof.
Given: XY
Prove: XY XY
Statements
1. XY
2. XY = XY
3. XY XY
Reasons
** Before beginning a proof, make sure to plan out your logic. Sometimes a plan will be given,
but NOT always**
Right Angle Congruence Theorem: _________________________________________________
___________________________________________________________.
Hypothesis:
Conclusion:
Congruent Complements Theorem:_________________________________________________
______________________________________________________________________________
_____________________________________________________________________________.
Hypothesis:
Conclusion:
Example 3: Given: 1 and 2 are supplementary, and
1
3
Prove: 3 and 2 are supplementary.
Plan: Use the definitions of supplementary and congruent angles and substitution to show that
m 3 + m 2 = 180°. By the definition of supplementary angles, 3 and 2 are supplementary