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Triangles
Types of Triangles
Methods of Proving
Triangles Congruent
SSS
Line Segments
in Triangles
Median
Acute
Right
SAS
Obtuse
ASA
Altitude
Scalene
HL
Isosceles Δ Theorem
P
AAS
(chap 7)
Q
If isosceles Δ,
PQ is a median ⇔ PQ is an altitude ⇔ PQ is an ∠ bisector
Isosceles
Equilateral
Median
Definition: If two polygons are
congruent polygons then all of
their corresponding sides are
congruent and all of their
corresponding angles are
congruent.
CPCTC Corresponding parts
of congruent triangles are
congruent.
If segments are radii of the
same or congruent circles, they
are congruent.
C = 2π r = π d
A =πr2
Two points determine a line.
If a segment is a median, then it
goes from a vertex of a
triangle…
• and divides the opposite side
into two congruent segments.
• and bisects the opposite side.
• to the midpoint of the opposite
side.
Altitude
If two sides of a triangle are
congruent, then the angles
opposite those sides are
congruent.
If two angles of a triangle are
congruent, then the sides
opposite those angles are
congruent.
•
•
If a segment is an altitude, then
it goes from a vertex of a
triangle…
• and forms right angles with the
opposite side (or its extension).
• and is perpendicular to the
opposite side.
• and forms a 90° angle with the
opposite side.
If a triangle is equilateral, then
it is also equiangular.
If a triangle is equiangular,
then it is also equilateral.
If two or more sides of a triangle
are not congruent, then the
largest angle is opposite the
longest side, etc.
If two or more angles of a
triangle are not congruent, then
the longest side is opposite the
largest angle.