ページ1:

Constructing Triangles and Finding Angles.
1 Type of triangles
Grouping according to sides
•
Equilateral triangle 3 equal sides
• Isoscelects triangle : 2 equal sides
d
Scalene triangle
0
•
: No equal sides
Grouping according to angle
Acute-angled triangle: All 3 angles are
-
Obtuse angled triangle One angle is an
Right
:
angled triangle: One
acute angles
obtuse angle
angle is a right angle
ELEGANT ELLI
STRAWBERRIES
& CREAM
125400
OLIPOP
Strawberry
Vanilla
60°
Equilateral triangle
Each angle = 60°
2 Angles of triangles
Isosceles Triangle
The andes opposite
the equal sides are
equal. These angle are
called the base angles of
the triangle.
The sum of the angles of a triangle is 180°
Za+b+LC = 180°
Example: In triangle STU, <STU = 55°
Find TSU
S
90°
Right-angled triangle
The sum of the two
acute angles = 90°
a
and <SUT
=
78°
ZTSU
180°- (55°+78°)
=
47°

ページ2:

Finding unknown angles in triangles
1 In triangle DEF, <EDF = 68° and < DFE = 71°
Find DEF
180
= ZEDF+<DFE + <DEF
180
<DEF =
68° 71+LDEF
-
180 (6871) = 41°
The sum of the angles of a triangle is 180
2 In triangle ABC, <ABC = 40° and <ACB = 36°
Find BAC
180° = CABC + <ACB + <BAC
180°.
ZBAC
40 +36 +<BAC
=
180 - (40+36)
D
68°
A
79°
F
40°
= 104°
B.
36°
C
new
3 In triangle ABC
Find <BAC
=
ZABC = 63°
and BCA
= 22°
9
180° ABC <BCA + <BAC
180 = 63+22+BAC
ZBAC 180 (63+22) = 95°
XYZ is an isosceles triangle and ZYXZ = 42°
Find LXYZ
180
180°
=
equal
ZYXZ+ZXYZ + ZYZX'
42°
180°
-
M
42°
=
138/2
=
69°
M
138°
.: LXYZ = M/2
5 XYZ is an isosceles triangle
and ZYXZ 45° Find ZXZY
=
ZXZY = 180°-(45+45°)
90°
42°
Iso sceles triangle
The angles opposite
the equal sides are
equal. These angle are
called the base angles of
the triangle.
KLM is an equilateral triangle and <KNM - 110°
Find NML
ZNML 180-(60+70°)
=
=
50°
Y
N
60°
60°
Equilateral triangle
Each angle = 60°
180-110°
70°
=
60°
M