Important Vocabulary Acute Triangles- A triangle in which all of the angles are acute angles Bisector- Cuts something in half to where each side is equal to each other Congruent Triangles- Triangles that have their corresponding parts congruent Equiangular Triangle- A triangle with all angles congruent Equilateral Triangle- A triangle with all sides congruent Hypotenuse- The side of a right triangle opposite the right angle Isosceles- A triangle with at least two sides congruent Legs of a Right Triangles- Opposite of the hypotenuse Obtuse Triangles- A triangle with an obtuse angle Right Triangle- A triangle with a right angle Scalene- A triangle with no sides congruent
Classifying Triangles by Angles Right triangles- has a right angle in it
Obtuse Triangle- has at least one obtuse angle
Acute Triangle- has at least one acute angle
Classifying Triangles by Sides Scalene Triangle- No sides are equal
Isosceles Triangle- Two sides are congruent
Equilateral Triangle- All sides are equal
Theorems for chapter 4 Angle sum theory- The sum of the measures of the angles of a triangle is 180 Third angle theorem- If 2 angles of a triangle congruent to 2 angles of another triangle, then the 3rd pair of a triangle is congruent Exterior angle sum theorem- the measure of an exterior angle is the sum of it’s two remote interior angles Isosceles Triangle theorem- angles opposite the legs of an isosceles triangle are congruent (base angles congruent)
Proving Right angles are congruent Theorems Hypotenuse-Leg theorem (HL) - from SAS
Leg-Angle theorem (LA) – from AAS
Leg-Leg theorem (LL) – from SAS
Hypotenuse-Angle theorem (HA) – from AAS
Postulates for Proving Triangles Congruent Side-Side-Side Postulate- If three sides of a triangle are congruent to three sides of another triangle, then the triangles are congruent by SSS.
Side-Angle-Side Postulate- If two sides of a triangle are congruent to two corresponding sides of another triangle and the included angles congruent, then the triangles are congruent by SAS.
Angle-Side-Angle Postulate- If two angles of a triangle and the included side are congruent to two angles and the included side of another, then the triangles congruent by ASA.
Angle-Angle-Side Postulate- If two angles and there non-included sides are congruent to two angles and their non-included side of another triangle, then the triangles are congruent AAS.
Coordinate Proofs 1.) 2.) 3.) 4.)
Use the origin as a vertex of the triangle Place at least one side of the triangle on an axis Keep the triangle in 1st quadrant whenever possible Use correlation that makes compilations as simple as possible