Chapter 4 – Congruent Triangles
4.1 Triangles and Angles
(theorems 4.1-4.2)
Classifying Triangles
Classification by Sides
Equilateral Triangle
Isosceles Triangle
_____________________
Scalene Triangle
__________________________
______________________
Classification by Angles
Acute Triangle
Right Triangle
________________
Obtuse Triangle
________________
Equiangular Triangle
___________________
____________________
Each point joining the sides of a triangle is called a ____________. The plural (more than one) of vertex
is ______________. Label the vertices of
ABC.
A
B
C
There are two sides that are _______________, or beside, vertex B. These two sides are ______ and
______. Side ________ is the side ___________________ of vertex B.
Chapter 4 – Congruent Triangles
Right and Isosceles Triangles
Right
Isosceles
In a right triangle, the sides that form the right
In an isosceles triangle, the two congruent sides
angle are called the ________. The side opposite
are called the _______. The third side is called the
the right angle is called the __________________.
___________.
Label the legs and hypotenuse of the right triangle.
Label the legs and base of the isosceles triangle.
Interior and Exterior Angles
The sum of the measures of the interior angles of a triangle is __________. (Triangle Sum Theorem 4.1)
The measure of an exterior angle of a triangle is equal to the ________ of the measure of the two
______________________ interior angles. (Exterior Angle Theorem 4.2)
Using Angle Measures of Triangles
Find the value of x.
Find the value of x.
65o
2xo
xo
xo
(2x + 10)o
Chapter 4 – Congruent Triangles
4.2 Congruence and Triangles
(theorems 4.3-4.4)
Identifying Congruent Figures
When two figures are congruent, there is a correspondence between their _____________ and
_____________ such that corresponding angles are ______________ and corresponding sides are
__________________.
D
S
E
Congruence Statement:
Corresponding Angles:
F
DEF ≅
RST
EFD ≅
STR
FDE ≅
TRS
DFE ≅
RTS
EFD ≅
STR
FDE ≅
TRS
R
T
There are many different ways to
write the congruence statement for
the two triangles, BUT NOTICE the
corresponding angles are
______________ in corresponding
positions.
Corresponding Sides:
If two angles of _______ triangle are congruent to two angles of ______________ triangle, then the
third angles are ___________________________. (Third Angles Theorem 4.3)
Chapter 4 – Congruent Triangles
4.3/4.4/4.6 Proving Triangles are Congruent
(postulates 19-21, theorems 4.5, 4.8)
Congruence Postulates/Theorems
There are 5 ways to prove that two triangles are congruent:





Tips for finding out if one of these postulates/theorems can be used:

__________ all information given.

Mark ______________ angles with congruence marks.

Mark _______________ sides with congruence marks.

If there are ________________________, see if that will give you any extra information.
4.6 Isosceles and Equilateral Triangles
(Theorems 4.6-4.7)
Isosceles Triangles
If two sides of a triangle are congruent, then the angles opposite them are ___________________.
Label the isosceles triangle with the appropriate marks.
M (0, 160)
4.7 Triangles and Coordinate Proof
Using Congruent Triangles in the Coordinate Plane
MLO ≅
L
KLO
Find the coordinates of point L.
O
K (160, 0)