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POSTULATE
Polygon Congruence Postulate
SSS
Two polygons are congruent if and only if:
 If the corresponding sides of one
triangle are congruent to the
corresponding sides of another
triangle then the triangles are
congruent.
 Each pair of corresponding sides are
congruent
 Each pair of corresponding angles are
congruent
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POSTULATE
POSTULATE
SAS
ASA
 If two sides and their included
angle of a triangle are congruent
to two sides and their included
angle of another triangle, then
the triangles are congruent.
 If two angles and the included side
in one triangle are congruent to two
angles and the included side in
another triangle, then the two
triangles are congruent.
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POSTULATE
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THEOREM
THEOREM
Unit 4
HL
AAS
 If the hypotenuse and a leg of a
right triangle are congruent to
the hypotenuse and a leg on
another right triangle, then the
two triangles are congruent.

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PROPERTIES
Unit 4
If two angles and the non-included
side of one triangle are congruent
to two angles and the nonincluded side of another triangle,
then the triangles are congruent.
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POSTULATE
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Isosceles Triangle
Corresponding parts of
congruent triangles are
congruent.
 AB = AC (legs)
 BC is base
 Angle C and Angle B are base
angles.
 Angle A is vertex angle.
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COROLLARY
THEOREM
Unit 4
Isosceles Triangle Theorem
 Base angles of an isosceles triangle
are congruent. (angle 2 and 3)
The measure of each angle of an
equilateral triangle is 60°.
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 If two angles of a triangle are
congruent then the sides opposite
the angles are congruent.
THEOREM
COROLLARY
Unit 4
The bisector of the vertex angle of an
isosceles triangle is the perpendicular
bisector of the base.
A diagonal of a parallelogram divides the
parallelogram into two congruent triangles.
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THEOREM
THEOREMS
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Opposite sides of a parallelogram are
congruent.
 If two pairs of opposite sides of a
Opposite angles of a parallelogram are
congruent.
quadrilateral are congruent, then the
quadrilateral is a parallelogram.
 If one pair of opposite sides of a
quadrilateral is parallel and congruent,
then the quadrilateral is a parallelogram.
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THEOREM
Consecutive angles of a parallelogram are
supplementary.
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THEOREM
The diagonals of a parallelogram bisect
each other.
 If the diagonals of a quadrilateral bisect
each other, then the quadrilateral is a
parallelogram.
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Rhombus is?
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Rectangle is?
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THEOREM
A rhombus is a parallelogram.
A rectangle is a parallelogram.
 If one pair of adjacent sides of a
 If one angle of a parallelogram is a right
parallelogram is congruent, then the
parallelogram is a rhombus.
angle, then the parallelogram is a
rectangle.
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THEOREM
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THEOREM
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The diagonals of a rhombus are
perpendicular.
The diagonals of a rectangle are
congruent.
 If the diagonals of a parallelogram bisect
 Housebuilder Theorem: If the
the angles of the parallelogram then the
parallelogram is a rhombus.
diagonals of a parallelogram are
congruent, then the parallelogram is a
rectangle.
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THEOREM
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 If the diagonals of a parallelogram are
perpendicular, then the parallelogram is a
rhombus.
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THEOREMS
 A square is a rectangle.
THEOREM
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The diagonals of a kite are perpendicular.
 A square is a rhombus.
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Unit 4
Diagonals of a Square
Triangle Midsegment Theorem
 Congruent
 A midsegment of a triangle is parallel
to a side of the triangle and has a
measure equal to half the measure of
that side.
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THEOREM
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THEOREM
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 Perpendicular bisectors of each other
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THEOREM
THEOREM
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Triangle Inequality Theorem
Euler Path
The sum of the lengths of any two sides
of a triangle is greater than the length of
the third side.
A graph contains an Euler path if and
only if there are at most two odd
vertices.
AB + BC > AC
BC + AC > AB
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AC + AB > BC
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