Download Proving Triangles Congruent

Postulate = Conjecture
Proving Triangles Congruent
1. State what is given in the problem
2. Mark angles or sides congruent if stated specifically in the proof
3. State angles or sides congruent and give reason why
a. Reason should be a definition, conjecture, if you find yourself having to explain
why it is not right and try a different method.
4. You then should have some kind of combination or sides and angles to use one of the
conjectures, SSS, SAS, ASA, AAS
5. State the triangles are congruent, make sure vertices are in the correct order, using one of
the postulates
If they state something in the given it has to specifically state a side congruent to a side or and
angle congruent to an angle in order to be able to mark it on the picture or use it for one of the
postulates, because what they give isn’t necessarily enough.
1. If they give you two triangles sharing a side
a. The shared side will be congruent because of the property reflexive
2. If they state that a point is the midpoint of a segment or side
a. The segment with the midpoint is now divided into two congruent parts
b. The parts are congruent because of the definition of midpoint
3. If they give you a picture where two lines cross
a. The angles opposite each other are congruent
b. The reason why is vertical angles
4. If they state that two segments are perpendicular
a. You know perpendicular segments form right angles
b. Set the two right angles congruent to each other and the reason is right angles
5. If they state that a segment bisects an angle
a. The angle that is bisected is now cut into two congruent angles
b. Set each new angle congruent to each other and the reason is definition of bisect
6. If they state two segments bisect each other
a. The segments are now cut into two pairs or congruent segments
b. Set each pair of segments congruent to each other and the reason is definition of
bisect
7. If they state that two lines are parallel
a. Set the two sets of angles congruent and reason if AI
8. Given a triangle is isosceles
a. State two sides congruent based on def of Isosceles
b. State two angles congruent based on def of Isosceles