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Advanced Geometry
Triangle Congruence
Lesson 1
Triangles & Congruence
Classifying Triangles by Angles
acute triangle –
all acute angles
right triangle –
one right angle
obtuse triangle –
one obtuse angle
equiangular triangle –
all angles congruent
Classifying Triangles by Sides
scalene triangle –
no two sides are
congruent
isosceles triangle –
at least two sides
are congruent
equilateral triangle –
all sides are congruent
Example:
Find x and the measures of the unknown sides of
each triangle.
Example:
Find d and the measure of each side of equilateral
triangle KLM if KL = d + 2, LM = 12 – d, and
KM = 4d – 13.
Example:
ΔABC is isosceles with AB = AC. AB is three times
a number decreased by 2, BC is two less than five
times the number, and AC is one more than twice
the number. Find the measure of each side.
Angle Sum Theorem
The sum of the measures of the
angles of a triangle is 180.
Example:
Find the missing angle measures.
Example:
Find the missing angle measures.
Exterior Angle
Definition – an angle formed by one side of a
triangle and the extension of another side
1
2
3
4
Remote Interior Angle
Definition – the two interior angles of a triangle
not adjacent to a given exterior angle
Exterior Angle Theorem
The measure of an exterior angle of a triangle
is equal to the sum of the measures of the
two remote interior angles.
1
2
3
4
Example:
Find the measure of each numbered angle.
Congruent Triangles
same size &same shape
triangles will be transformed (turned, flipped, or
slid)
ALL corresponding
parts must be
congruent
Corresponding Parts
Example: Identify the congruent angles and sides and
the congruent triangles in each figure.
Example: Name the congruent angles and sides for
each pair of congruent triangles.
VBK  NXH
Example:
FGH  JKL , FG = 4, GH = 6, FH = 9,
and JL = 2x – 5. Draw and label a figure to show
the congruent triangles, and then find x.
Congruent Triangles
Two triangles are congruent if and only if
their corresponding parts are congruent
Corresponding Parts of Congruent
Triangles are Congruent
CPCTC
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