Download Writing a Proof in Chapter 4

Writing a Proof in Chapter 4
All of the proofs in Chapter 4 involve proving triangles congruent. In writing these proofs, you should
first mark given information on the diagram. Also, make sure to look for information that is given on the
diagram such as shared sides and vertical angles. Shared sides with be added to the proof as a segment
congruent to itself and the reason would be “Reflexive Property.” Vertical angles are congruent by the
“Vertical Angles Theorem.”
If there is not enough information yet to prove triangles congruent, look at other given information such
as midpoints or bisectors. If there is a midpoint, it cuts a segment into two congruent segments and the
reason would be “Definition of a Midpoint.” If there is a bisector, see what was bisected, a segment or
an angle. If an angle is bisected, it is cut into two congruent angles and you would use “Definition of an
Angle Bisector” as the reason. If a segment is bisected, it is cut into two congruent segments and you
would use “Definition of a Segment Bisector” as the reason. Other things to look for are parallel lines. If
lines are parallel, often there will be alternate interior angles or corresponding angles that are
congruent when formed by parallel lines cut by a transversal. The reason for these congruent angles
would either be “Alternate Interior Angles Theorem” or “Corresponding Angles Theorem.”
When there are perpendicular segments, you either need to show that the right angles formed are
congruent, using the theorem that states “All right angles are congruent,” or you will use them to show
that the triangles are right triangles so that you can use “Hypotenuse-Leg Theorem,” usually written as
“HL.”
If a statement says that two triangles are congruent, the reason must be one of the five ways to prove
triangles are congruent: SSS, SAS, ASA, AAS, or HL. After you have proven triangles are congruent, you
know that all of their remaining corresponding parts are congruent. The reason for this is “Definition of
Congruent Triangles” or “CPCTC” which means “Corresponding parts of congruent triangles are
congruent.”