Download Congruent-Triangles

CONGRUENT
TRIANGLES
Congruence
• We know…
• Two SEGMENTS are congruent if they’re the same length.
2”
2”
• Two ANGLES are congruent if they have the same measure.
60°
60°
Third Angles Theorem
• If two angles of one triangle are congruent to two angles
of a second triangle, then:
• The third angles are also congruent
• The two triangles are SIMILAR (but not necessarily CONGRUENT)
Triangle Congruence
• Congruence: Two triangles are CONGRUENT if (and only
if) they have three pairs of congruent sides and three
pairs of congruent angles.
Corresponding Parts
• If two triangles are congruent, then:
• The corresponding sides are the sides that are congruent
• The corresponding angles are the angles that are congruent
Minimum Information for Congruence
• There are three angles and three sides to every triangle,
so there are six pieces of information.
• We need to know that at least THREE pieces of
information match (with some restrictions).
Theorem #1: SSS
• If the side lengths of two triangles are congruent, then the
triangles are congruent.
Theorem #2: SAS
• If two sides and the angle between them are congruent,
then the triangles are congruent.