Download Triangle - Humble ISD

TOPIC 6-1: TRIANGLE BASICS
TERM
DESCRIPTION
A plane, closed figure formed
Triangle
by 3 segments joining 3 noncollinear points.
SKETCH
A triangle is made up of three components:
Q
Vertices:
Sides:
R
P
Angles:
One way to classify triangles is by the length of its sides.
TERM
DESCRIPTION
SKETCH
Scalene
A triangle with no congruent
sides.
Isosceles
A triangle with 1 pair of congruent
sides.
Equilateral A triangle with all three sides
congruent.
EXAMPLE 1 Classify each of the triangles by SIDES.
a)_______________
b)_______________
c)_______________
The sum of the measures of the interior angles of a triangle is 180  .
Triangles can also be classified by the measure of its interior
angles.
TERM
DESCRIPTION
A triangle in which all three
angles have a measure less
than 90°
Acute
Obtuse
A triangle in which one angle
has a measure greater than 90°
Right
A triangle in which one angle
has a measure equal to 90°
SKETCH
A triangle in which all angles
Equiangular are equal
EXAMPLE 2 Classify the triangles by ANGLES.
a)___________
b)___________ c)___________
60
60
75
60
85
d)___________
35
20
115 30
EXAMPLE 3 Find the measure of the third angle of a triangle, if
the first angle has a measure of 66 and the second
angle measures 37.
EXAMPLE 4 Find the measure of each angle of RST.
R
3x
(x+40)
x
S
T
mR = __________
mS = __________
mT = __________
R
EXAMPLE 5 Find the value of ‘x’.
x
x = __________
S x
x T
The triangle in EXAMPLE 5 is an equiangular triangle.
Based on this example, we can say that each angle of an equiangular
triangle is 60  .
J
EXAMPLE 6 Find the value of ‘x’.
(3x+2)
x = __________
K
(2x+3)
J and L in EXAMPLE 6 would be classified as acute angles.
Since their sum is 90  , we can say that the acute angles of a right
triangle are complementary.
L
An exterior angle of a triangle is formed by one side of the triangle,
and the extension of an adjacent side.
To find the measure of an exterior angle of a triangle, add the two
remote interior angles.
D
EXAMPLE 7 Find the measure of 1.
80
1 2
E
40 F
m  1 = ____________
EXAMPLE 8 In XYZ, mX = 63 and mZ = 64, find mZYR.
Z
X
Y
R
m  ZYR = ____________
EXAMPLE 9 In EFG, mG = (11x – 2) , mF = (8x + 4)°, and
mFEH = (17x + 10)°. Find mF.
F
G
E
m  F = ____________
H