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Congruent Triangles. If two triangles are congruent, then all of the parts of one triangle are congruent to the corresponding parts of the other triangle. This means that the corresponding sides and the corresponding angles are congruent.
The sum of the measure of the angles of a triangle is 180o Corollary The acute angles of a right triangle are complementary. Exterior angle theorem An exterior angle of a triangle is equal in measure to the sum of the measures of its two remote interior angles. Triangle Proportionality Theorem
Isosceles Triangle Theorem If two sides of a triangle are congruent, then the angles opposite those sides are congruent. Corollary 4-1 - A triangle is equilateral if and only if it is equiangular. Acute triangle - A triangle with all acute angles. Equiangular triangle - A triangle with all angles congruent.
Definition In a protractor geometry {P, L, d, m}, we say ∠ABC is an acute angle if m(∠ABC) < 90, a right angle if m(∠ABC) = 90, and an obtuse angle if m(∠ABC) > 90. We say angles ∠ABC and ∠DEF are supplementary if. m(∠ABC) + m(∠DEF ) = 180. and we say angles ∠ABC and ∠DEF are complementary if. m(∠ABC) + m(∠DEF ) = 90.
Angle Theorems Alternate Exterior Angles Theorem. If a transversal intersects two parallel lines, then the alternate exterior angles are congruent. Converse also true: If a transversal intersects two lines and the alternate exterior angles are congruent, then the lines are parallel.
Complementary angles TWO angles that add up to 90° , for example. and b are complementary angles because the angles 50° and in the triangle add up to 180°. d are adjacent complementary angles because they lie nextto each other, forming a right angl.
The Angle Sum Theorem for triangles states that the sum of the interior angles of a triangle is always_______. It does not matter what kind of triangle (ex. Acute, obtuse, right) when you add
