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Name: ____________________________________________________________
Date: _________________________
Period: _______
Chapter 2: Keyword Proofs
Topic 7: Unknown Angles in Proofs
One of the main goals in Geometry is to develop the ability to think critically, to draw valid conclusions based upon
observations and proven facts. Many times we can do this through proofs.
Some helpful properties in solving proofs:
Substitution Property: If two expressions are equal to the same “thing” (number, variable, etc.) then they are
________________ to each other.
If
and
then ________________
Subtraction Property: Just like we can subtract when solving a linear equation, we can ______________________ using
variables. The same idea applies.
If
, then
Helpful Hint for proofs (that you will use a lot!!!): if an angle is not labeled, it is perfectly ok to label it with a letter
or number! You are allowed to use anything in your proof, as long as it’s properly __________________________________.
For most proofs, it is easiest to write ________________________ and ______________________ columns. This helps organize all
of our thoughts.
Example:
1.) Given the labeled diagram to the right, prove that
.
Name: ____________________________________________________________
Date: _________________________
Period: _______
2.) Prove that the vertical angles,
, are congruent. Use the diagram below to help you.
3.) Given the diagram on the right, prove that
.
Name: ____________________________________________________________
4.) Given the diagram on the right, prove that
Date: _________________________
Period: _______