Download Lesson 4.2 Notes

Chapter 4: Congruent
Triangles
Lesson 2: Angles of Triangles
 The sum of the
measures of the
angles of a triangle
is always 180
degrees.
 The acute angles of
a right triangle are
complementary
 There can be at
most one right or
one obtuse angle in
a triangle
 Third Angle Theorem
 If two angles of one
triangle are
congruent to two
angles of another
triangle, then the
third angles of the
triangles are also
congruent. X
A
B
Y
Z
C
If  A   X, and  B   Y, then
 C   Z.
Interior and Exterior Angles of
Triangles
 Exterior angle: formed by one side of
a triangle and the extension of
another side
 Remote Interior angle: the interior
angles farthest from the exterior
angle (remote interior angles are not adjacent to the exterior
angle)
Remote interior
angles
Exterior
angle
2
An exterior angle is equal to the
sum of its remote interior angles.
ex:  1 +  2 =  4
1
3
4
Anticipation Guide: read each statement. State whether the
sentence is true or false. If the statement is false- rewrite it with
the correct term in place of the underlined word
 The acute angles of a right triangle are
supplementary
 The sum of the measures of the angles of any
triangle is 100
 A triangle can have at most one right angle or
acute angle
 If two angles of one triangle are congruent to two
angles of another triangle, then the third angle of
the triangles are congruent
 The measure of an exterior angle of a triangle is
equal to the difference of the measures of the two
remote interior angles
 If the measures of two angles of a triangle are 62
and 93, then the measure of the third angle is 35
 An exterior angle of a triangle forms a linear pair
with an interior angle of the triangle
SOFTBALL The diagram
shows the path of the
softball in a drill
developed by four players.
Find the measure of each
numbered angle.
Find the measure of each
numbered angle.
GARDENING Find the measure
of FLW in the fenced flower
garden shown.
The piece of quilt fabric is in the shape of a
right triangle. Find the measure of ACD.
Find the measure of
each numbered
angle.
Find the measure of each numbered angle.