Vocabulary
CPCTC
corresponding parts of congruent triangles are congruent
CPCTC can be used BEFORE the triangles are proven congruent
FALSE
two angles and the included side are congruent
ASA
When ordering a proof, what MUST be proven before CPCTC can be used?
the triangles must be proven congruent
An imaginary "helping line" drawn through the center pf a triangle to help separate it into two congruent parts.
an auxiliary line
CPCTC proves triangles congruent
FALSE
two sides and the EXCLUDED angle are congruent
Hint: this does NOT prove triangles congruent
SSA
When ordering a proof, this REASON is almost ALWAYS used DIRECTLY after a triangle congruence postulate
CPCTC
a line that bisects an angle in a triangle and goes through the midpoint of the opposite side
median
an isosceles triangle has three congruent sides and three congruent angles
FALSE
An isosceles triangle has TWO congruent sides and TWO congruent angles
when two sides and the included angle are congruent
SAS
When ordering a proof, this is ALWAYS used before CPCTC
Proving triangles congruent/a Triangle Congruence Postulate
If two SIDES of a triangle are congruent, then the ANGLES opposite those sides are also congruent
Isosceles triangle theorem
an obtuse triangle has ONE obtuse angle
TRUE
Triangles ABC and DEF are isosceles triangles that are congruent. If SIDE AB and SIDE EF are congruent, which angles are also congruent and by what theorem?
Angles A and F are congruent by the isosceles triangle theorem
BEFORE you try to order a proof, you should always do this FIRST
If two ANGLES of a triangle are congruent, then the SIDES opposite those angles are also congruent
CONVERSE of the isosceles triangle theorem
the reflexive property makes the segment/line of reflection congruent to itself
TRUE
Triangles ABC and DEF are isosceles triangles that are congruent. If angle A is congruent to angle F, which SIDES are also congruent and by what theorem?
Sides AB and EF are congruent by the CONVERSE of the isosceles triangle theorem.
When shown a picture of multiple triangles within a bigger triangle, this should ALWAYS be your first step be after reading the question
Draw/separate the triangles