Download 4.1 Triangles and Angles

7.G.5 Triangles and
Angles
Geometry
Mr. Nealey
7th Grade
Standard/Objectives:
Objectives:
• Classify triangles by their sides and
angles.
• Find missing angle measures in triangles
DEFINITION: A triangle is a figure formed
by three line segments joining three noncollinear points.
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Names of triangles
Triangles can be classified by the
congruency of their sides.
Equilateral
—3
congruent
sides
Isosceles
Triangle—2
congruent
sides
Scalene—
no
congruent
sides
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Triangles by Angles
• Triangles can also be classified by
the size of their largest angle. All
triangles have at least 2 acute
angles, the smallest of the 3.
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Acute Triangle
All 3 angles are acute angles
m ABC = 70.26 
m CAB = 41.76 
m BCA = 67.97 
B
C
A
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Right
Triangle
• Has only 1 right
angle
Obtuse
Triangle
• Has only 1 obtuse
angle
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Sum of the Angles
• Label your triangle
with angles A, B,
and C.
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Sum of the Angles
• Tear the angles
off your triangle,
being careful to
preserve the
corners.
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Sum of the Angles
• Connect the tips of
your triangle
together.
• When you add all 3
angles, what does
the sum appear to
be?
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Sum of the Angles
• What is the sum of
the interior angles
of any triangle?
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Finding the missing Angle
• What is the sum of
the interior angles
of any triangle?
• 180 Degrees
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Find the Missing Angle
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Find the Missing Angle
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Triangles
• Use P.430 in the Course 2 Book #3-23
• Find missing angles using 180 degrees
• Identify the Triangles by their sides and
angles.
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End of day 1…Day 2…
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Parts of a triangle
• Each of the three
points joining the
sides of a triangle is a
vertex.(plural:
vertices). A, B and C
are vertices.
• Two sides sharing a
common vertext are
adjacent sides.
• The third is the side
opposite an angle
Side
opposite
A
B
C
adjacent
adjacent
A
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Right Triangle
hypotenuse
• Red represents the
hypotenuse of a
right triangle. The
sides that form
the right angle are
leg
the legs.
leg
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Isosceles Triangles
• An isosceles triangle
can have 3 congruent
sides in which case it
is equilateral. When
an isosceles triangle
has only two congruent
sides, then these two base
sides are the legs of
the isosceles triangle.
The third is the base.
leg
leg
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Identifying the parts of
an isosceles triangle
•
About 7 ft.
5 ft
•
5 ft
Explain why ∆ABC is
an isosceles right
triangle.
In the diagram you
are given that C is
a right angle. By
definition, then
∆ABC is a right
triangle. Because AC
= 5 ft and BC = 5 ft;
AC BC. By
definition, ∆ABC is
also an isosceles
triangle.
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Identifying the parts of
an isosceles triangle
Hypotenuse & Base
•
About 7 ft.
•
5 ft
leg
5 ft
leg
Identify the legs and
the hypotenuse of
∆ABC. Which side is
the base of the
triangle?
Sides AC and BC are
adjacent to the right
angle, so they are
the legs. Side AB is
opposite the right
angle, so it is t he
hypotenuse. Because
AC BC, side AB is
also the base.
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Using Angle Measures of
Smiley faces are
Triangles
interior angles and
hearts represent the
exterior angles
B
A
C
Each vertex has a pair
of congruent exterior
angles; however it is
common to show only
one exterior angle at
each vertex.
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