Download - Lesson 4.2
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Lesson 4.2
Discover the properties of
Isosceles Triangles.
HOMEWORK:Lesson 4.2/1-11
QUIZ Tomorrow: 4.1 – 4.2
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Isosceles Triangle at least two sides have the same length
5 m
9 in9 in
4 in
5 m
5 m
3 miles 3 miles
3 miles
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Properties of an Isosceles Triangle
Has at least 2 equal sides
Has 2 equal angles
Has 1 line of symmetry
1
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Equilateral Triangle Isosceles Triangle with all three sides are
congruent
7 ft 7 ft
7 ft
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Parts of an Isosceles Triangle:
The vertex angle is the
angle between two congruent
sides
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The base angles are the angles opposite the
congruent sides
Parts of an Isosceles Triangle:
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The base is the side
opposite the vertex angle
Parts of an Isosceles Triangle:
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Isosceles Triangle Conjecture If a triangle is isosceles, then base angles
are congruent.
If then
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Converse of Isosceles Triangle Conjecture If a triangle has two congruent angles, then
it is an isosceles triangle.
If then
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Equilateral Triangle Conjecture An equilateral triangle is equiangular, and
an equiangular triangle is equilateral.
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Find the missing angle measures.
mb =
68˚
44˚ 68˚ a
b<68° and < a are base angles therefore they are congruent
ma =
m<b = 180 – 68 - 68
m<b = 180 -136
Triangle sum to find <b
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mc =
md =
Find the missing angle measures.
30.5˚
30.5˚
119˚
c d
Triangle sum = 180°180 = 119 + c + d180 – 119 = c + d61 = c + d
<c & <d are base angles and are congruent
<c = ½ (61) = 30.5<d = ½ (61) = 30.5
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mE =
mF =
mG =
Find the missing angle measures.
60˚
60˚
60˚ GF
EEFG is an equilateral triangleTherefore <E = <F = <G
180 /3 = 60
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Find mG.
Thus m<G = 22 + 44 = 66°And m<J = 3(22) = 66°
x = 22
Find the missing angle measures.
∆GHJ is isosceles< G = < J
x + 44 = 3x44 = 2x
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Find mN
Thus m<N = 6(8) = 48°.m<P = 8(8) – 16 = 48°
Find the missing angle measures.
6y = 8y – 16-2y = -16
y= 8
Base angles are =
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Using Properties of Equilateral Triangles
Find the value of x.
∆LKM is equilateral.m<K = m<L = m<M
Find the missing angle measures.
180/3 = 60°
2x + 23 = 602x = 37
x = 18.5°
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Using Properties of Equilateral Triangles
Find the value of y.
∆NPO is equiangular therefore, ∆NPO is also equilateral.
Find the missing side measures.
5y – 6 = 4y +12y – 6 = 12
y = 18
Side NO = 5(18) – 6 = 90ft
ftft
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Using the symbols describing shapes answer the following questions:
36o a
b
c
45o
d
Isosceles triangleTwo angles are equal
a = 36o
b = 180 – (2 × 36) = 108o
Equilateral triangleall angles are equal
c = 180 ÷ 3 = 60o
Right-angled triangle
d = 180 – (45 + 90) = 45o
Find the missing angle measures.
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q 36o
p
s
r
56o
Kite - Made up of 2 isosceles triangles
p = 36o
q = 180 – (2 * 36) = 108o
56 + (r + s) = 180o
(r + s) = 180 – 56 = 124
Because r = s
r = s = 124 ÷ 2 = 62o
Find the missing angle measures.
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a = 64o
b = 180 – (2 ×64o ) = 52o
c = dc + d = 180 - 72c + d = 108c = d = 54o
Equilateral trianglee = f = g = 60o
h = ih + i = 180 - 90h + i = 90h = i = 45o
Find the missing angle measures.
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p = 50o
q = 180 – (2 ×50o ) = 80o
r = q = 80o vertical angles are equalTherefore : s = t = p = 50o
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Properties of Triangles Properties of Triangles
a = b= c = 60o
d = 180 – 60 = 120o
e + 18 = a = 60
exterior angle = sum of remote interior angles
e = 60 – 18 = 42o
p = q = r = 60o
s = t = 180 - 43 = 68.5o
2
Find the missing angle measures.
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1) Find the value of x
2) Find the value of y
Find the missing angle measures.
1) x is a base angle180 = x + x + 50
130 = 2xx = 65°
2) y & z are remote interior angles and base angles of an isosceles
triangleTherefore: y + z = x and y = z
y + z = 80°y = 40°
50°
x°y°
D
C
B
A
z
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1) Find the value of x
2) Find the value of y
50E
DB
CA
yx
Find the missing angle measures.
2) y is the vertex angle
y = 180 – 100y = 80°
1) ∆CDE is equilateralAll angles = 60°
Using Linear Pair <BCD = 70°
x is the vertex anglex = 180 – 70 – 70
x = 40°
60°70°
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Lesson QuizFind each angle measure.
1. mR
2. mP
Find each value.
3. x 4. y
5. x
Find the missing measures.
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Lesson Quiz con’t
6. The vertex angle of an isosceles triangle measures (a + 15)°, and one of the base angles measures 7a°. Find a and each angle measure. (Make a sketch)
Find the missing angle measures.
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Lesson Quiz Solutions
1. 28°
2. 124°3. 204. 65. 266. a = 11; 26°; 77°; 77°
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Homework
In your textbook:•Lesson 4.2/ 1-11