Download Analyzing Isosceles Triangles

4 – 6: Analyzing Isosceles Triangles
Expectation:
G1.2.2: Construct and justify arguments and solve
multi-step problems involving side length, angle
measure, perimeter and area of all types of
triangles.
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4-6: Analyzing Congruent Triangles
Isosceles Triangles
In an isosceles triangle, the 2 congruent sides
are called the legs and the third side is called
the base. Label the base and the legs on the
triangle below.
C
A
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B
4-6: Analyzing Congruent Triangles
Isosceles Triangles
In an isosceles triangle, the 2 angles at the
ends of the base are referred to as base
angles and the angle where the legs meet is
called the vertex angle. Label the base
angles and the vertex angle on the triangle
below.
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4-6: Analyzing Congruent Triangles
Look at the isosceles triangles below.
What appears to be true about the base
angles?
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4-6: Analyzing Congruent Triangles
Isosceles Triangle Theorem
If 2 sides of a triangle are congruent,
then the angles opposite those sides
are __________.
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4-6: Analyzing Congruent Triangles
What is the measure of ∠α in the
diagram below?
A.
B.
C.
D.
E.
20°
55°
70°
75°
110°
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α
10
10
55°
4-6: Analyzing Congruent Triangles
Triangle ABC is isosceles. Calculate the value of
x.
C
5x+23
A
10x-7
B
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4-6: Analyzing Congruent Triangles
Given the information below, what
can we conclude about AB and AD?
A
B
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C
4-6: Analyzing Congruent Triangles
D
Justify your claim!
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4-6: Analyzing Congruent Triangles
Isosceles Triangle Converse
Theorem
If 2 angles of a triangle are congruent,
then the sides opposite those angles
are ___________.
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4-6: Analyzing Congruent Triangles
Solve for x.
7x+12
38
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12x-18
38
4-6: Analyzing Congruent Triangles
Equilateral Triangle Corollary:
A triangle is equilateral iff it is
________________.
Equilateral Triangle Angle Corollary:
Each angle of an equilateral triangle has
measure of ____.
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4-6: Analyzing Congruent Triangles
Given: Triangle ABC is equilateral.
Prove: ∠A≅∠B≅∠C
C
A
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B
4-6: Analyzing Congruent Triangles
If CF ≅ KF, name 2 congruent
angles.
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4-6: Analyzing Congruent Triangles
If ∠10 ≅ ∠DFL, name 2 congruent segments.
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4-6: Analyzing Congruent Triangles
If m∠1 = 30°, determine the measures of
the other numbered angles.
7
3
1
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2
4
5
6 8
4-6: Analyzing Congruent Triangles
In ΔABC below, AB ≅BC, and the measure of
∠B is 55°. What is the measure of ∠C?
A.
B.
C.
D.
E.
27.5°
55°
62.5°
125°
cannot be determined from the given
information.
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4-6: Analyzing Congruent Triangles
Assignment
pages 225-227,
#15, 21, 27-30(all), 36, 47
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4-6: Analyzing Congruent Triangles