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Solve each equation.
1. x + 6 = 25
2. x + 7 + 13 = 33
3. 5x = 540
4. x + 10 = 2x
5. For the triangle below, use the Triangle
Angle-Sum Theorem to find the value of y.
Chapter 4: Congruent Triangles
Objectives:
To prove triangles are congruent given
information about their sides and
angles.
Use congruent triangles to solve reallife problems.
REVIEW: Triangles and Angles
Objectives:
Classify triangles by their sides and
angles
Find angle measures in triangles.
Triangles: figure formed by 3
segments joining 3 noncollinear
points.
CLASSIFICATION BY SIDES
(# of congruent sides)
Scalene Triangle-no congruent sides
Isosceles Triangle-at least 2 congruent sides
Equilateral Triangle-3 congruent sides
CLASSIFICATION BY ANGLES
(all triangles have at least two acute angles, the third angle
is used to classify)
EQUIANGULAR TRIANGLE – 3 congruent sides
(also acute)
• Vertex – each of the three points joining
the sides of a triangle.
• Adjacent sides – two sides sharing a
common vertex.
• Opposite side – the third side not
sharing the vertex
Definitions:
B
B
A
C
Interior angles –
angles inside the
triangle
A
Exterior angles –
angles that are
adjacent to the
interior angles.
C
Theorem: Triangle Sum Theorem
The sum of the measures of the interior angles of a
triangle is 180°.
mA  mB  mC  180
Theorem : Exterior Angle Theorem
1
The measure of an exterior angle of a triangle is equal
to the sum of the measures of the two nonadjacent
interior angles.
m1  mA  mB
Checkpoint?
1.
110°
(4x-7)°
x°
2. The measure of one acute angle of a
right triangle is five times the measure
of the other acute angle. Find the
measure of each acute angle.
4.1 Congruent Figures
Objectives:
Identify congruent figures and
corresponding parts.
Congruent figures – have exactly
the same size and shape
*Corresponding angles
and sides are congruent.
*3 ways to move a figure
on top of another
-Flip
-Slide
-Turn
******The order that the letters come in always display
the corresponding relationship.
Congruent Figures
ABC
QTJ. List the congruent corresponding parts.
List the corresponding vertices in the same order.
Angles: A
Q
B
T
C
J
List the corresponding sides in the same order.
Sides: AB
QT
BC
TJ
AC
QJ
Checkpoint?
In the diagram, ABCD  KJHL , find:
Find the value of x.
A
9
91°
B
L
(5y-12)°
86°
D
6
113°
C
K
4x-3
H
J
Theorem 4.1: Third Angles Theorem
If two angles of one
triangle are congruent
to two angles of another
triangle, then the third
angles are also congruent.
If A  D and B  F
then C  E
Checkpoint?
G
K
(4x-9)°
F
J
100°
45°
H
I
Find the value of x.
Congruent Figures
Can you conclude that
the figure below?
ABC
List corresponding vertices in the same order.
If
ABC
CDE, then BAC
DCE.
The diagram above shows BAC
DEC, not DCE.
Corresponding angles are not necessarily congruent, therefore you
cannot conclude that ABC
CDE.
CDE in
E
H
58°
G
58°
F
J
Decide whether the triangles are congruent.
Homework
Pages 182-184
# 1-23, 24-27, 30-35, 38-40