Identifying Congruent Triangles OBJECTIVES - Triangle classification by parts - Angle Sum Theorem & Exterior Angle Theorem - CPTC,SSS,SAS,ASA,and AAS Theorems - Problem solving by eliminating possibilities -Equilateral & Isosceles triangles

Classifying triangles By angle measures Right one angle 90° Obtuseone angle obtuse Acuteall angles acute equiangularall 3 By side lengths Equilateral 3 sides Isosceles 2 sides Scaleneno lengths same Parts of an Isosceles Triangle Vertex Angle 2 sides  leg leg Base angle  Base angle Base is side opposite vertex

Measuring angles in triangles The sum of the measures of the 3 angles of a triangle always equals 180º If 2 In a right triangle, the 2 acute angles are complementary There can be at most 1 obtuse or 1 right angle in a Δ The measure of an exterior angle = the measure of the two remote interior angles: Remote interior angles Exterior angle

Congruent triangles: CPCTC Two Δ’s are congruent if and only if their corresponding parts are congruent (all sides & all angles) corr parts 1 2 Congruence of triangles is: reflexive (parts to self) symmetric transitive

If 2 triangles are congruent: 1 The congruence statement statement tells which parts of triangle 1 ‘match up’ or correspond to the parts of triangle 2. Means ORDER IS VERY IMPORTANT

Proving Δ’s congruent: SSS & SAS & ASA Given: 2 Δ’s (match up sides/angles that are alike) If 3 sides 2 sides & an included angle  OR 2 angles & an included side  are congruent  THEN the 2 Δ’s are congruent ** remember-- in two column proofs the ‘if’ part matches what you know & goes in the left column. The ‘then’ part goes in the right column & gives direction towards the statement to be proven.

Congruent triangles: AAS ‘Read around’ the vertices of a triangle: if an angle & another angle & a side not between them are congruent to the corresponding parts of another triangle,  THEN the triangles are congruent Mark the given parts on your triangles to see which theorem or postulate to use. There WILL be a clue to get you started B D F E C A

Isosceles triangles If 2 sides are ,  then angles opposite them are B A C If 2 sides are ,  then angles opposite them are If 2 angles of a triangle are , then the sides opposite are A triangle is equilateral if and only if it is equiangular Each angle of an equiangular triangle measures 60°

Example: Given: ΔTEN is an isosceles triangle with base TN 1 2 3 4 T C A N Given: ΔTEN is an isosceles triangle with base TN Prove: ΔTEA ΔNEC 1. ΔTEN is an isosceles triangle with base TN 1. Given 2.Def Isosceles 3.Given 4. ΔTEA ΔNEC 4.AAS End with what you are to prove