Download Understanding Triangle Basics

Aim: Understanding Triangles
Do Now:
SAT Question
What must be the complement of the
supplement of an obtuse angle?
A. An acute 
B. A right 
C. An obtuse  D. A straight 
E. A reflex 
Aim: Understanding Triangles - I
Course: Applied Geometry
Triangles
A triangle is a three sided polygon enclosing three
angles.
The sum of the measure of the angles of a
triangle is 180 degrees (1800)
Classified According to Angles
Right Triangle - has one right angle
Acute Triangle - has three acute angles
Obtuse Triangle - has one obtuse angle
Applied Geometry
Aim: Understanding Triangles - I
Equiangular Triangle
- has three Course:
equal
angles
Model Problems
Identify each triangle using its angles.
ABC has angles that measure 100o, 40o and
isosceles
400.
DEF has angles that measure 60o, 70o and
acute
50o.
STU has angles that measure 60o, 60o and
equilangular
60o.
XYZ has angles that measure 130o, 20o and
obtuse
30o.
BAC in ABC measure 600 and is equal to
equilateral
ABC.
BAC in ABC measure 90o and BAC and
Course: Applied Geometry
Aim:equal
Understanding
rt. triangle
BCAare not
to Triangles
each- Iother.
Triangles
Classified According to Sides
3 equal
sides
2 equal
sides
No equal
sides
C
•An
Equilateral
Triangle is also
Equiangular
600
A
600
Aim: Understanding Triangles - I
600
Course: Applied Geometry
B
Model Problems
Identify each triangle as equilateral, isosceles
or scalene.
ABC has sides that measure 3, 3, and 3
equilateral
units in length.
HIJ has sides that measure 4, 4, and 7 units
isosceles
in length.
STU has sides that measure 2, 3, and 4 units
in length.
scalene
Line segment AB in ABC is equal to line
segment AC and 4 times the length of line
isosceles
segment BC.
Line segment XY in XYZ is equal to line
equilateral
segments YZAim:and
XZ.
Course: Applied Geometry
Understanding Triangles - I
Model Problems
What type of triangle is each of the following?
equilateral/equiangular
obtuse/scalene
isosceles right triangle
Aim: Understanding Triangles - I
Course: Applied Geometry
Model Problems
Identify the measure of each unknown angle
and the type of triangle.
B
x=?
x
x = 180 – (55 + 46) = 79
scalene and acute
46
55
C
A
B
x=?
x
25
115
A
A
C
50
50
y=?
C
x = 180 – (25 + 115) = 40
scalene and obtuse
y
B
x = 180 – (50 + 50) = 80
isosceles and acute
C
60
A
t=?
60
Aim:
t
B
x = 180 – (60 + 60) = 60
equilateral/equiangular
Course: Applied Geometry
Understanding Triangles - I
Right Triangle ABC
B
If B = 450, then A = ?
450
If B = 160, then A = ?
740
If A = 33.50, then B = ? 56.50
C
What is true about A & B?
complementary angles
A
The sum
L of the
In right triangle LMN, find the value
measure of the
of x and the measure of L and N.
0
x of
angles
a
0
30
x + 2x + 90 = 180
triangle is 1800.
3x + 90 = 180
600 0
3x
=
90
2x
x = 30
M
N
L = 300 N = 600
Aim: Understanding Triangles - I
Course: Applied Geometry
Find the value of x, y, and z
G
To find x, use FJG:
210
390
65 + 39 + x = 180
104 + x = 180
0
x
orFJG
=
76
0
650 x0 y
z0
F
J
H
To find y, use FJH, a straight angle:
FJG + GJH = 1800
760 +
y = 1800
y = 1040
To find z, use GJH:
104 + 21 + z = 180
125 + z = 180
z or FHG = 550
Aim: Understanding Triangles - I
Course: Applied Geometry
In triangle ABC, find the value of x
and mB and C.
The sum of the
measure of the
angles of a
triangle is 1800.
C
A
760
x + 15
2x -10 B
x + 15 + 2x - 10 + 76 = 180
x + 2x + 15 - 10 + 76 = 180
3x + 81
= 180
3x
= 99
x
= 33
C = x + 15 = 480
B = 2x -10 = 530
33+ 15 = 480
66 -10 = 560
Aim: Understanding Triangles - I
Course: Applied Geometry
Model Problems
Identify the measure of each unknown angle.
A
J
36
C
1
61
2
5 F
118 6 3
46
E
D
81
4
m3 =
66
B
m4 =
H
7
8 G
m1 =
m2 =
51
m5 =
m6 =
m7 =
m8 =
Aim: Understanding Triangles - I
Course: Applied Geometry