10Special TheoremsThe 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.
11More TheoremsIf 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.
12Prove: The two acute angles of a right triangle are complementary BGiven: ABC, <A is a right angleCAStatementsReasons1. 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 complementary1. Given2. All right angles equal 90 3. The sum of the angles of a triangle equal 180 4. Substitution from step 2 into step 35. Subtraction property6. If the sum of the measures of two angles equals 90 , then the angles are complementary.