Geometry:
Partial Proofs with Congruent Triangles
Recall, that we do proofs in two columns.
In the left-hand column we
write statements that lead from the given information
to what needs proved.
In the right-hand column we
give a reason for each statement.
Further recall, that the reason for the first
Given while the reason
statement is always ______
for each succeeding statement must be a
_________,
theorem
postulate or ________.
definition _________
These are the definitions, postulates and
theorems that we will use as reasons in our
proofs.
DEFINITIONS:
If two lines are perpendicular, then
they intersect to form right angles.
A midpoint of a segment is
a point which divides the segment into two
congruent segments
DEFINITIONS:
An angle bisector is
a ray which divides the angle into two congruent
angles.
Vertical angles are
the nonadjacent angles formed when two lines
intersect.
DEFINITIONS:
Alternate interior angles are
two angles on opposite sides of the transversal and
between the parallel lines.
Corresponding angles are
two angles in the same position relative to the
transversal and the two parallel lines.
POSTULATES:
Corresponding Angles Postulate: If two angles
are corresponding angles, then
they are congruent.
Reflexive Postulate:
Any angle or segment is conguent to itself.
THEOREMS:
Vertical Angle Theorem: If two angles are vertical angles,
then
they are congruent.
Alternate Interior Angle Theorem: If two angles are
alternate interior angles, then
they are congruent.
Right Angle Theorem: If two angles are right angles then,
they are congruent.
In addition to the above definitions,
postulates and theorems, you will use the
four congruent shortcuts, _____,
SSS _____,
SAS
_____,
ASA and _____,
AAS as your reason for why
two triangles are congruent.
Examples: Complete each proof by supplying
the missing statements and reasons.
HA // DN , HA  DN
Given
AHN & HND are AIAs
AHN  HND
HN  HN
HND  NHA
AIAT
Reflexive
SAS
Given
VTS & VTU are rt. angles
RAT
SVT  UVT
VT  VT
Def. of bisects
Reflexive
ASA