Triangles

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Triangles Congruence

• Advanced Geometry
• Triangle Congruence
• Lesson 1

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Classifying Triangles by Angles
acute triangle all acute angles
right triangle one right angle
equiangular triangle all angles congruent
obtuse triangle one obtuse angle
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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
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Example
Find x and the measures of the unknown sides of
each triangle.
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Example
Find d and the measure of each side of
equilateral triangle KLM if KL d 2, LM 12
d, and KM 4d 13.
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Example
?ABC 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.
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Angle Sum Theorem The sum of the measures of the
angles of a triangle is 180.
Example
Find the missing angle measures.
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Example
Find the missing angle measures.
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Exterior Angle
Definition an angle formed by one side of a
triangle and the extension of another side
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2
3
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Remote Interior Angle
Definition the two interior angles of a
triangle not adjacent to a given exterior angle
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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.
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2
3
4
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Example
Find the measure of each numbered angle.
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Congruent Triangles
same size
same shape
triangles will be transformed (turned, flipped,
or slid)
ALL corresponding parts must be congruent
Corresponding Parts
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Example Identify the congruent angles and sides
and the congruent triangles in each figure.

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Example Name the congruent angles and sides for
each pair of congruent triangles.
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Example
and JL 2x 5. Draw and label a figure to
show the congruent triangles, and then find x.
, FG 4, GH 6, FH 9,
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Congruent Triangles
Two triangles are congruent if and only if their
corresponding parts are congruent
Corresponding Parts of Congruent Triangles are
Congruent
Corresponding Parts of Congruent Triangles are
Congruent
CPCTC