Geometry: Chapter 4
4.1: Apply Triangle Sum Properties
A triangle is a polygon with three sides. A triangle
with vertices A, B, and C is called “triangle ABC”.
Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 217.
Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 217.
Ex. 1: Classify the triangle shown below
by measuring its sides and angles.
Image taken from: http://upload.wikimedia.org/wikipedia/commons/thumb/e/e4/Triangle-acute.svg/460px-Triangle-acute.svg.png
Ex. 2: Classify triangle ABC by its sides and
by its angles.
Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 218.
Ex. 2: Classify triangle ABC by its sides and by its angles.
Step 1: Use the distance formula to find the side lengths.
( x2  x1 ) 2  ( y2  y1 ) 2
(4  2) 2  (1  6) 2  4  49  53  7.3
(2  5) 2  (6  4) 2  49  4  53  7.3
(5  4) 2  (4  1) 2  81  25  106  10.3
( 53) 2  ( 53) 2  ( 106) 2 , So this is a right triangle.
Since two of the sides have the same length, the triangle
is isosceles. This is a right isosceles triangle.
ANGLES
When the sides of a polygon are extended,
other angles are formed. The original angles
are the interior angles. The angles that
form linear pairs with the interior angles are
the exterior angles.
Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 218.
Theorem 4.1: Triangle Sum Theorem
The sum of the measures of the interior
angles of a triangle is 1800.
Theorem 4.2 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.
Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 220.
Ex. 3. Find the mDEF.
Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 219.
Ex. 3. Find the mDEF.
Using the Exterior Angle Theorem (Theorem
4.2), I know that:
3x + 6= 80 + x
3x- x= 80-6
2x = 74
x = 37
mDEF = 3x + 6= 3(37) + 6 = 1170
Corollary to the Triangle Sum Theorem
The acute angles of a right triangle are
complementary.
Ex. 4
The support for the skateboard ramp shown
forms a right triangle. The measure of one acute
angle in the triangle is five times the measure of
the other. Find the measure of each acute angle.
Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 220.
A Right Triangle has two legs and a
hypotenuse. The side opposite the right
angles is the hypotenuse of the angle.
An Isosceles Triangle has two legs and a base.
The two sides that are congruent are called
the legs.