Transcript Honors Geometry Intro. to Geometric Proofs

Honors Geometry
Intro. to Geometric Proofs
Before we can consider geometric
proofs, we need to review
important definitions and
postulates from Unit I.
“If and only if” (abbreviated iff)
means that both a statement and
its converse is true.
Definitions:
An angle is a right angle iff
it has a measure of 90 degrees.
Two lines are perpendicular iff
they intersect to form a right angle.
A ray bisects an angle iff
the ray divides the angle into
two congruent angles.
Two angles are complementary iff
they have a sum of 90 degrees.
Two angles are supplementary iff
they have a sum of 180 degrees.
A point is a midpoint of a segment iff
the point divides the segment into
two congruent segments.
You must also be able to use the
definition of a linear pair to
identify a linear pair in a figure.
Postulates:
Segment Addition Postulate:
If R is between P and Q, then
PR + RQ = PQ
Angle Addition Postulate:
If S is in the interior of PQR, then
mPQS  mSQR  mPQR
Linear Pair Postulate:
If two angles form a linear pair,
then the angles are supplementary.
Examples: Complete,
and give a reason for,
each statement.
FMD  DMC
Defintion of angle bisector
mFME  mBMC  90
Definition of complementary
Examples: Complete,
and give a reason for,
each statement.
mEMC  90
Definition of right angle
ME  MC
Definition of perpendicular
Examples: Complete,
and give a reason for,
each statement.
AM  MC
Definition of midpoint
Example: Complete this partial proof.
JG  JI
mGJI  90
Given
Def. of Perpendicular
Def. of right angle
Angle Addition Post.
Substitution prop.
1 and 2 are complementary Def. of complementary