Classify triangles by sides

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Transcript Classify triangles by sides

Classify triangles by sides
No congruent sides
Scalene triangle
At least two sides congruent
Isosceles triangle
Three congruent sides
Equilateral triangle
Classify triangles by angles
3 acute angles
Acute triangle
1 right angle
Right triangle
1 obtuse angle
Obtuse triangle
3 congruent angles
Equiangular triangle
Triangle Sum Theorem
The sum of the measures of the interior
angles of a triangle is
180o.
Exterior Angle Theorem
The measure of an exterior angle of a
triangle is equal to
the sum of the measures of the two
nonadjacent interior angles.
Corollary to the Triangle Sum
Theorem
The acute angles of a right triangle are
complementary.
Base Angles Theorem
If two sides of a triangle are congruent,
then the angles opposite them are
congruent.
Converse to Base Angles Theorem
If two angles of a triangle are congruent,
then the sides opposite them are congruent.
Corollary to Base Angles Theorem
If a triangle is equilateral, then it is
equiangular.
Corollary to Base Angles Converse
If a triangle is equiangular, then it is
equilateral.
Triangle Inequalities (4)
The largest angle is opposite the largest
side.
The largest side is opposite the largest
angle.
The smallest angle is opposite the smallest
side.
The smallest side is opposite the smallest
angle.
Triangle Inequality Theorem
The sum of the lengths of any two sides of a
triangle is
greater than the length of the third side.
Hinge Theorem
If two sides of one triangle are congruent to
two sides of another triangle,
and the included angle of the first is larger
than the included angle of the second,
then the third side of the first is larger than
the third side of the second.
Converse of the Hinge Theorem
If two sides of one triangle are congruent to
two sides of another triangle,
and the third side of the first is longer than
the third side of the second,
then the included angle of the first is larger
than the included angle of the second.