Advanced Geometry Triangle Congruence Lesson 1 Triangles Congruence

Advanced Geometry Triangle Congruence Lesson 1 Triangles & Congruence

Classifying Triangles by Angles acute triangle – all acute angles right triangle – one right angle obtuse triangle – one obtuse angle equiangular triangle – all angles congruent

Classifying Triangles by Sides scalene triangle – no two sides are congruent isosceles triangle – at least two sides are congruent equilateral triangle – all sides are congruent

Example: Find x and the measures of the unknown sides of each triangle.

Example: Find d and the measure of each side of equilateral triangle KLM if KL = d + 2, LM = 12 – d, and KM = 4 d – 13.

Example: ΔABC is isosceles with AB = AC. AB is three times a number decreased by 2, BC is two less than five times the number, and AC is one more than twice the number. Find the measure of each side.

Angle Sum Theorem The sum of the measures of the angles of a triangle is 180. Example: Find the missing angle measures.

Example: Find the missing angle measures.

Exterior Angle Definition – an angle formed by one side of a triangle and the extension of another side 1 2 3 4 Remote Interior Angle Definition – the two interior angles of a triangle not adjacent to a given exterior angle

Exterior Angle Theorem The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles. 1 2 3 4

Example: Find the measure of each numbered angle.

Congruent Triangles same size & same shape triangles will be transformed (turned, flipped, or slid) ALL corresponding parts must be congruent Corresponding Parts

Example: Identify the congruent angles and sides and the congruent triangles in each figure.

Example: Name the congruent angles and sides for each pair of congruent triangles.

Example: , FG = 4, GH = 6, FH = 9, and JL = 2 x – 5. Draw and label a figure to show the congruent triangles, and then find x.

Congruent Triangles Two triangles are congruent if and only if their corresponding parts are congruent Corresponding Parts of Congruent Triangles are Congruent CPCTC