Download Notes 4.1

Sec 4.1 Apply Triangle Sum Properties
VOCABULARY
Triangle
________________________________________________________________________
Interior angles: angles inside the figure.
Ex: angles 4, 6, and 7.
Exterior angles: angles created by extending
the sides of a figure,
lie outside the figure.
Ex: angles 1, 2, 3, 5, 8, 9, 10, 11, 12.
1
2
5 6
9 10
4
3
7
8
11 12
Corollary to a theorem
________________________________________________________________________
________________________________________________________________________
CLASSIFYING TRIANGLES BY SIDES
Scalene Triangle
Isosceles Triangle
Equilateral Triangle
____ congruent sides
At least ____ congruent sides
____ congruent sides
CLASSIFYING TRIANGLES BY ANGLES
Acute Triangle
Right Triangle
Obtuse Triangle
Equiangular Triangle
____ acute angles
____ right angle
____ obtuse angles
____ congruent angles
Notice that an equilateral triangle
is also isosceles. An equiangular
triangle is also acute.
Example 1 Classify ∆RST by its sides. Determine if the triangle is a right triangle.
Step 1 Use the distance formula
RS = __8.1__
(5- -3)
2
 (2 - 3 )
2
x2  x1  2  y2  y1 2
 8.1
ST = _________
(
)
to find the side lengths.
RT = ________
)  (
2
2
) 
(
)  (
2
2
) 
Step 2 Check for right angles.
The slope of RT is __________.
The slope of ST is ____________.
The product of the slopes is ______, so RT  ST and RTS is a ________ angle.
Therefore, ∆RST is a ____________ _ triangle.
THEOREM 4.1: TRIANGLE SUM THEOREM
mA + mB + mC = ___________
The sum of the measures of the interior angles of a triangle is ______.
THEOREM 4.2: EXTERIOR ANGLE THEOREM
Angles A, B and C are interior angles. A and B are called REMOTE INTERIOR angles because they are
far away from the exterior angle at C.
m1 = m_ __ + m__ _
The measure of an exterior angle of a triangle is equal to the sum of the measures
of the two remote interior angles.
Example 2
Use the diagram at the right to find the measure of DCB, A and 1 .
Solve
3x+16 = 52 + 2x
x = 36
so mA=2(36) = 72,
m1 = 180-(52+72) = 56.
mDCB= 3(36)+16 = 124.
To check your answers:
The exterior angle = the sum of the 2 remote interior angles. 124 = (52+72) smile!
Example 3
Use the diagram at the right to find the measure of DCB.
Solution
Step 1 Write and solve an equation to find the value of x.
3x  9 = x + 73
x = _____
Exterior Angle Theorem
Solve for x.
Step 2 Substitute x = ____ in 3x  9 to find mDCB.
3x  9 = 3  ____  9 = _____.
The measure of DCB is _____.
COROLLARY TO THE TRIANGLE SUM THEOREM
mA + mB = _____
The acute angles of a right triangle are _____________.