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Geometry Final Study Guide
Chapter 3 Review
Things You Should Know
Triangle Congruency Postulates
 Different Types of Segments
 Types of Triangles
 Other Useful Theorems
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SSS Postulate
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If there exists a
correspondence
between the vertices of
two triangles such that
three sides of one
triangle are congruent
to the corresponding
sides of the other
triangle, the two
triangles are congruent
Tick marks show
congruent parts
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ASA Postulate
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If there exists a
correspondence between the
vertices of two triangles such
that two angles and the
included side of one triangle
are congruent to the
corresponding parts of the
other triangle, the two
triangles are congruent
It is illegal to use ASA to
prove triangles congruent if
the congruent side is not
between the two congruent
angles
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SAS Postulate
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If there exists a
correspondence between the
vertices of two triangles such
that two sides and the
included angle of one
triangle are congruent to the
corresponding parts of the
other triangle, the two
triangles are congruent
Remember, the congruent
angle must be between the
two congruent sides to use
this postulate
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HL Postulate
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If there exists a correspondence
between the vertices of two right
triangles such that the
hypotenuse and a leg of one
triangle are congruent to the
corresponding parts of the other
triangle, the two right triangles
are congruent
If you know two sides of one
right triangle are congruent to
two sides of another right
triangle, then you can prove the
right triangles congruent no
matter where the sides are
positioned
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Types of Segments
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Auxiliary lines: Lines that are not drawn in on
the original diagram that the “proover” draws
in himself/herself
 These lines are represented as dotted lines
 Median: A line segment drawn from any
vertex of the triangle to the midpoint of the
opposite side
 Every triangle has three medians
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Types of Segments Cont.
Altitude: A line segment drawn from any
vertex of the triangle to the opposite
side
 Every triangle has three altitudes
 In an isosceles triangle, the median
drawn from the vertex angle to the base
of the triangle is also the altitude of the
triangle
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Types of Triangles
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Equilateral triangle: All sides are
congruent
 Equiangular triangle: All angles are
congruent
 Equiangular triangles and equilateral
triangles are the same
 Isosceles triangle: Triangle in which at
least two sides are congruent
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Types of Triangles Cont.
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Acute triangle: A triangle in which all
angles are acute
 Obtuse triangle: A triangle in which one
of the angles is obtuse
 Right triangle: One of the angles of this
type of triangle is a right angle
 A triangle cannot have more than one
obtuse angle
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CPCTC
Stands for, “Corresponding Parts of
Congruent Triangles are Congruent”
 Example: Two congruent triangles were
proved congruent by SAS
 These triangles will be known as
triangle ABC and triangle XYZ
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CPCTC Cont.
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Because the two triangles are
congruent, the corresponding sides AB
and XY are congruent as well
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Radii Theorem
All radii of a circle are congruent
 A radius is a segment that extends from
the center of the circle to any point on
the circle
 This theorem is very useful in proofs
such as these, where triangles are
inside circles.
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Angle-Side Theorems
If two sides of a triangle are congruent,
the angles opposite the sides are
congruent
 Can be shortened to “If sides, the
angles” when used in a proof
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Angle-Side Theorems Cont.
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If two angles of a triangle are congruent,
the sides opposite the angles are
congruent
 Can be shortened to “If angles, then
sides” when used in proofs
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