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**Report by Jennifer Johnson**

Triangles Report by Jennifer Johnson

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What is a Triangle? A polygon Three sides Three angles

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**Types of Triangles By Sides By Angles Scalene Isosceles Equilateral**

Acute Obtuse Right

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**A triangle with no sides congruent.**

Scalene A triangle with no sides congruent.

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**A triangle with at least 2 congruent sides**

Isosceles A triangle with at least 2 congruent sides

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**A triangle with all sides congruent**

Equilateral A triangle with all sides congruent

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**A triangle with all acute angles**

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**A triangle with one obtuse angle**

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**A triangle with one right angle**

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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.

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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.

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**Prove: The two acute angles of a right triangle are complementary**

B Given: ABC, <A is a right angle C A Statements Reasons 1. ABC is a triangle, <A is a right angle. 2. If <A is a right angle, then it’s measure = 90 3. m<A + m<B + m<C = 180 . 4. 90+ m<B + m<C = 180 5. m<B +m<C = 90 6. <B and <C are complementary 1. Given 2. All right angles equal 90 3. The sum of the angles of a triangle equal 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.

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