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Triangles
Report by
Jennifer Johnson
What is a Triangle?
• A polygon
• Three sides
• Three angles
Types of Triangles
By Sides
Scalene
Isosceles
Equilateral
By Angles
Acute
Obtuse
Right
Scalene
A triangle with no sides congruent.
Isosceles
A triangle with at least 2 congruent sides
Equilateral
A triangle with all sides congruent
Acute
A triangle with all acute angles
Obtuse
A triangle with one obtuse angle
Right
A triangle with one right angle
Special Theorems
• The sum of the angles of a triangle equals
180 degrees.
• If a triangle is an isosceles triangle, then the
angles opposites the congruent sides are
congruent.
• If a triangle is an obtuse triangle, then the
side opposite the obtuse angle is the longest
side of the triangle.
More Theorems
• If a triangle is an equilateral triangle, the all
angles of the triangle are congruent and
equal 60 degrees.
• The two acute angles of a right triangle are
complementary.
Prove: The two acute angles of a right triangle are complementary
Given:
ABC, <A is a right angle
B
A
Statements
1. ABC is a triangle, <A is a right
angle.
2. If <A is a right angle, then it’s
C
Reasons
1. Given
2. All right angles equal 90 
measure = 90 
3. m<A + m<B + m<C = 180 .
3. The sum of the angles of a
4. 90+ m<B + m<C = 180 
4. Substitution from step 2 into
step 3
5. Subtraction property
6. If the sum of the measures of
two angles equals 90  , then
the angles are complementary.
5. m<B +m<C = 90 
6. <B and <C are complementary
triangle equal 180 