Download Using Patterns and Inductive Reasoning

Triangles
Today’s Objectives
• To learn new strategies that will help find
the measures of angles in a triangle
• To review how to classify triangles
Types of Triangles (by sides)
• Equilateral
• Isosceles
• Scalene
Equilateral Triangles
• Definition:
– A triangle with three
congruent sides.
• Example:
Isosceles Triangles
• Definition:
– A triangle with two
congruent sides.
• Example:
Scalene Triangles
• Definition:
– A triangle with no
congruent sides.
• Example:
Types of Triangles (by angle)
• Equiangular
• Acute
• Right
• Obtuse
Equiangular Triangles
• Definition:
– A triangle with three
congruent angles.
• Example:
Acute Triangles
• Definition:
– A triangle whose
angles are all acute.
• Example:
Right Triangles
• Definition:
– A triangle with one
right angle.
• Example:
Obtuse Triangles
• Definition:
– A triangle with one
obtuse angle.
• Example:
Triangle Video
• Triangle video!!
Triangle Activity
1.
2.
3.
4.
Draw and cut out a large triangle.
Number all three angles of the triangle
Tear of the angles
Place the 3 angles adjacent to each other to
form one angle
•
•
Compare your results with a partner.
Draw conclusions about the sum
of the angles of a triangle.
Triangle Angle-Sum
The sum of the measures
of the angles of a
triangle is
always 180.
Find the measure of the
missing angle
< C = 57°
http://maths.fallibroome.cheshire.sch.uk/triangle.jpg
http://www.mathsisfun.com/geometry/images/triangle-missing-angle.gif
< a = 87°
x
< x = 45°
x
http://www.gizapyramid.com/basic_triangle_w-angles.gif
Practice
• Find all value for
missing angels:
<y +70+90=180
<y +160=180
<y=20
<x+40+90=180
<x+130=180
<x=50
Practice
• Find all value for
missing angels:
<x +83+41=180
<x +123=180
<x=56
<x and <y are vertical angels
and therefore, have the same
measure
Practice
• Find all value for
missing angels:
<x + 39 + 65=180
<x +104=180
<x=76
<y + <x = 180
<y +76 = 180
<y = 104
<z + <y + 21 = 180
<z + 104 +21 = 180
<z + 125 = 180
<z = 55
Find the following angle
measures.
B
45°
C 123°
57°
<FDC
<ADF
<FDC
<CDB
<CDBangles are
The
following
<D
74++106
90++angles
D57
==
180
180
The<D
following
are
+
123
+
45
=
180
supplementary
= 180°
<D
164++163
D ==
=180
180
supplementary
180°
+ 168angle
= 180
74 + <D
missing
= 180°
<D
D angle
==16
17= 180°
57 + missing
<Dangle
= 12= 106 °
Missing
Missing angle = 123°
F 106°
74°
A
D
Homework
Triangles