Download Geometry Notes G.6 Triangle Basics, Congruence Mrs. Grieser

Geometry Notes G.6 Triangle Basics, Congruence
Mrs. Grieser
Name: __________________________________________ Date: _______________ Block: ________
Triangle Basics

Definition: A triangle is a polygon with ______ sides.

A triangle with 3 ________ A, B, and C is written as ∆ABC.
Classify Triangles by Sides:
Scalene: No  sides
Isosceles: At least 2  sides
Equilateral: 3  sides
Classify Triangles by Angles:
Acute: 3 acute
angles
Right: 1 right
angle
Obtuse: 1 obtuse angle

Interior angles are those angles on the inside of a triangle.
Name interior angles: _______________________

Exterior angles are formed when the lines of the triangle are
extended. Name exterior angles:_____________________


Equiangular: 3 
angles
Triangle Sum Theorem
The sum of the measures of the interior angles of a triangle is
180o.
A corollary to a theorem is a statement that can be proved easily using the theorem.
Corollary to the Triangle Sum Theorem
The acute angles of a right triangle are complementary.
Exterior Angle Theorem
The measure of an exterior angle of a triangle is equal to the sum
of the measures of the two nonadjacent interior angles.
Examples:
a) Find x; classify the
∆
b) Find x; classify the
∆
c) Find mB , m1
d) Find the measures
of the numbered
s
Geometry Notes G.6 Triangle Basics, Congruence
Mrs. Grieser Page 2
Triangle Congruence
 In two congruent figures, all the
corresponding parts are congruent
(Corresponding Parts of Congruent Triangles
are Congruent: CPCTC).
 In polygons, this means corresponding sides
and angles are congruent.
 When writing congruence statements, always
list the congruent parts in the same order.
Third Angles Theorem
If two angles of one triangle are congruent to two angles of
another triangle, then the third angles are also congruent.



Properties of Congruent Triangles Theorem
Reflexive Property of Congruent Triangles
o For any ∆ ABC, ∆ABC  ∆ABC
Symmetric Property of Congruent Triangles
o If ∆ABC  ∆DEF, then ∆DEF  ∆ABC
Transitive Property of Congruent Triangles
o If ∆ABC  ∆DEF and ∆DEF  ∆JKL, then ∆ABC  ∆JKL
Examples:
a) Identify  parts:
angles:
b) ∆ABC  ∆DEF
Find x and y.
c) Find x.
sides:
conclusion:
___________
d) Find x.
e) Given the figure at right, prove ACD  CAB
Statements
1) AD  CB,DC  BA
2) AC  AC
ACD  CAB;
3)
CAD  ACB
4) B  D
5) ACD  CAB
You Try...
a) In the diagram,
QRST  WXYZ . Find the
value of x and y.
Reasons
1)Given
2) ____________________
3) Given
4) ____________________
5) Def. of  figures
b) FGHK  STUV .
Find the value of x
and mG .