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Geometry Section 4-1A
Angles Inside the Triangle
Pg. 242
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Tessellations
Tessellation:
A repeating pattern of figures that completely covers a
plan region without gaps or overlaps.
We will soon investigate several geometric figures to
see whether or not they can be used to tessellate a plane.
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3
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Triangles
Triangle:
A figure formed by three segments that connect three
noncollinear points.
vertex
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Label the parts of the
triangle.
side
side
vertex
vertex
side
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Triangle Classification by Sides
Scalene Triangle – no congruent sides.
Isosceles Triangle – 2 congruent sides.
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Equilateral Triangle – All sides congruent.
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Triangles
vertex angle
Non-right triangles
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base
angle
base
base
angle
leg
Right triangles
leg
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Try It:
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Try it: Two angles of a triangle measure
40o and 58o. What is the measure of the
third angle? 180 – (40 + 58) = 82o
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Triangle Classification by Angles:
Acute Triangle – all angles acute.
Obtuse Triangle – 1 obtuse angle.
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Equiangular Triangle – All angles congruent.
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Triangle Angle-sum Theorem
Triangle Angle-Sum Theorem:
The sum of the measures of the angles of a
triangle is 180o.
http://mathopenref.com/triangleinternalangles.html
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Exercises
Name and classify each triangle, using both
angle and side classification.
J
N
L
M
#1, 2
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rJLM
Isosceles
Right
O
P
rNOP
Scalene
Obtuse
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Exercises
Name and classify each triangle, using both
angle and side classification.
P
Q
T
#3,4
4.3
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S
R
rPQR
Equilateral
Equiangular
3.6
5.0
U
rSTU
Scalene
Acute
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Exercises
Is it possible for each type of triangle to exist?
If so, sketch it. If not, explain why.
Obtuse Isosceles
#6
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Exercises
Is it possible for each type of triangle to exist?
If so, sketch it. If not, explain why.
Right Equilateral
#7
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Not possible. In an
equilateral triangle, every
angle is 60o.
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Exercises
Is it possible for each type of triangle to exist?
If so, sketch it. If not, explain why.
Right Scalene
#8
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Exercises
FP is one side of a triangle on the grid. List the
possibilities for the third vertex if the triangle is a:
a. obtuse B, C, D, E, V, W, X, Y
#9
b. right
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c. isosceles H, L, M, N, O, R
G, H, I, J, L, Q, R, S, T
d. Suppose the third vertex of the triangle is chosen
randomly from the points shown in red. What is the
probability that the triangle will be a right triangle?
3
4
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Exercises
Find the measure of angle 1.
1
1
#11,
12
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72o
40o
57o
180 – (40 + 72) = 68o
180 – (90 + 57) = 33o
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Exercises
Find the measure of angle 1.
81o
#13,
14
1
a
41ao
50o
b
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1
50o
41o
a and b are
corresponding ’s
and are @.
180 – (81 + 41) = 58o
50o
a must = 40o.
a + b = 90o
therefore, b = 50o
and c = 50o
180 – (50 + 50) = 80o
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Homework: Practice 4-1A
#1-3 – You cannot “name” them. Mistake
on worksheet.
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