Table Of Contents
Page One: Chapter Four Vocabulary Page Two: Identify and Classify Triangles by angles and sides. Page Three: Apply the Angle sum theorem and exterior angles sum theorem. Page Four: Solve Problems involving congruent triangles. Page Five: Prove congruent triangles using SSS and SAS Postulates. Page Six: Prove congruent triangles using ASA and AAS Postulates. Page Seven: Prove right triangles are congruent. Page Eight: Solve problems involving isosceles triangles & Solve Coordinate Proofs
Chapter 4 Vocabulary Acute Triangles- all angles equal less than 90 degrees
Base Angles- Two angles formed by the base and one of the congruent sides. Congruent Triangles- Same Measure of sides and angles. Coordinate Proof- uses figures in a coordinate plane and algebra to prove a geometric concept. Corollary- a statement that can be easily proven using a theorem. Equiangular Triangle- An acute triangle with all angles congruent. Equilateral Triangle- All sides are congruent. Exterior Angle- formed by one side of a triangle and the extension of another side. Hypotenuse- the side of a triangle that the legs are attached to. Isosceles Triangles- at least two sides are congruent. Obtuse Triangles- One angle in the triangle is obtuse. Perpendicular Bisector- a bisector in a triangle perpendicular to the base forming two 90 degree angles. Remote Interior Angles- the interior angles not adjacent to the given exterior angle. Right Triangle- a triangle with one angle that equals 90 degrees Scalene- No sides of the triangle are congruent. Vertex Angle- Angle formed by the congruent sides.
Chapter Four identifying and classifying triangles by angles and sides.
Right Triangles are triangles with one angle adding up to 90 degrees. The other two angles will add up to less than 90 degrees. Acute Triangles are triangles where all the angles add up to less than 90 degrees. Obtuse Triangles are triangles where one angle adds up to greater that 90 degrees.
Isosceles triangles are equal on two sides. Scalene Triangles are not equal on any sides. Equilateral Triangles has all congruent sides.
Chapter Four Apply the angle sum theorem and the exterior angle sum theorem. The sum of the measures of the angles of a triangle is 180 Angle Sum Theorem. Third Angle Theorem: If two angles of a triangle are congruent to two angles of another triangle then the third proof angles are
congruent. Exterior Angle Sum Theorem: The measure of an exterior angle is the sum of its two remote interior angles. EX:
The sum of angle A and angle B should add together to get the Exterior Angle. The Exterior angle and its adjacent side should add together to equal 180 degrees. EX2:
A Corollary is the acute angles of a right triangle, which are complementary.
The corollaries in the image above would be angles one and two.