Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
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