Identifying Congruent Triangles

1
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

2
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
3
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 ?
• The measure of an exterior angle the measure of
  the two remote interior angles

Remote interior angles
Exterior angle?
4
Congruent triangles CPCTC

• Two ?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

5
If 2 triangles are congruent
2
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
6
Proving ?s congruent SSS SAS ASA

• Given 2 ?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 ?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.
7
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
8
Isosceles triangles
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

9
Example
E
1
2
3
4
T
N
C
A

• Given ?TEN is an isosceles triangle with base
  TN
• Prove ?TEA ?NEC

• 1. ?TEN is an isosceles triangle with base TN 1.
  Given
• 
  2.Def Isosceles
• 
  3.Given
• 4. ?TEA ?NEC 4.AAS

End with what you are to prove