Use isosceles and equilateral triangles
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CH 4.7
USE ISOSCELES AND EQUILATERAL TRIANGLES
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In this section…We will use the facts that we know about
isosceles and equilateral triangles to solve for missing sides or angles.
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What do you know about an isosceles triangle?There are two congruent sides in an isosceles triangle and two congruent angles.
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What do you remember about an equilateral triangle?All of the sides and angles should be congruent.
The angles in an equilateral triangle always equal 60o.
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Base Angles TheoremIf two sides of a triangle are congruent, then
the base angles are also congruent.Base angles are the angles at the ends of the 2
congruent segments.So, in the diagram angles B and C are
congruent.
Base angle Base angle
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Converse to the Base Angles TheoremIf two angles in a triangle are congruent,
then the triangle is an isosceles triangle.
That means that the 2 sides of the triangles are also congruent.
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Find the value of x.This is an isosceles triangle, so the 2 sides are congruent…
5x + 5 = 35
5x = 30
x = 6
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This is an isosceles triangle, so the 2 angles are congruent…
9x = 72
x = 8
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x + x + 102 = 1802x + 102 = 180
2x = 78x = 39
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The sum of the interior angles is 180…
x + 7 = 55
x = 48
55 + 55 + y = 180
110 + y = 180y = 170
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If this is an isosceles triangle then what are the two congruent angles
x = 45
9y = 45
y = 5
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How would you find the values of x and y?
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What are all of the missing angles?
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