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CH 4.7 USE ISOSCELES AND EQUILATERAL TRIANGLES

CH 4.7 USE ISOSCELES AND EQUILATERAL TRIANGLES. In this section… We will use the facts that we know about isosceles and equilateral triangles to solve

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Page 1: CH 4.7 USE ISOSCELES AND EQUILATERAL TRIANGLES. In this section… We will use the facts that we know about isosceles and equilateral triangles to solve

CH 4.7

USE ISOSCELES AND EQUILATERAL TRIANGLES

Page 2: CH 4.7 USE ISOSCELES AND EQUILATERAL TRIANGLES. In this section… We will use the facts that we know about isosceles and equilateral triangles to solve

In this section…We will use the facts that we know about

isosceles and equilateral triangles to solve for missing sides or angles.

Page 3: CH 4.7 USE ISOSCELES AND EQUILATERAL TRIANGLES. In this section… We will use the facts that we know about isosceles and equilateral triangles to solve

What do you know about an isosceles triangle?

There are two congruent sides in an isosceles triangle and two congruent angles.

Page 4: CH 4.7 USE ISOSCELES AND EQUILATERAL TRIANGLES. In this section… We will use the facts that we know about isosceles and equilateral triangles to solve

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.

Page 5: CH 4.7 USE ISOSCELES AND EQUILATERAL TRIANGLES. In this section… We will use the facts that we know about isosceles and equilateral triangles to solve

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

Page 6: CH 4.7 USE ISOSCELES AND EQUILATERAL TRIANGLES. In this section… We will use the facts that we know about isosceles and equilateral triangles to solve

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.

Page 7: CH 4.7 USE ISOSCELES AND EQUILATERAL TRIANGLES. In this section… We will use the facts that we know about isosceles and equilateral triangles to solve

Find the value of x.

This is an isosceles triangle, so the 2 sides are congruent…

5x + 5 = 35

5x = 30

x = 6

Page 8: CH 4.7 USE ISOSCELES AND EQUILATERAL TRIANGLES. In this section… We will use the facts that we know about isosceles and equilateral triangles to solve

This is an isosceles triangle, so the 2 angles are congruent…

9x = 72

x = 8

Page 9: CH 4.7 USE ISOSCELES AND EQUILATERAL TRIANGLES. In this section… We will use the facts that we know about isosceles and equilateral triangles to solve

x + x + 102 = 180

2x + 102 = 180

2x = 78

x = 39

Page 10: CH 4.7 USE ISOSCELES AND EQUILATERAL TRIANGLES. In this section… We will use the facts that we know about isosceles and equilateral triangles to solve

The sum of the interior angles is 180…

x + 7 = 55

x = 48

55 + 55 + y = 180

110 + y = 180

y = 170

Page 11: CH 4.7 USE ISOSCELES AND EQUILATERAL TRIANGLES. In this section… We will use the facts that we know about isosceles and equilateral triangles to solve

If this is an isosceles triangle then what are the two congruent angles

x = 45

9y = 45

y = 5

Page 12: CH 4.7 USE ISOSCELES AND EQUILATERAL TRIANGLES. In this section… We will use the facts that we know about isosceles and equilateral triangles to solve

How would you find the values of x and y?

Page 13: CH 4.7 USE ISOSCELES AND EQUILATERAL TRIANGLES. In this section… We will use the facts that we know about isosceles and equilateral triangles to solve

What are all of the missing angles?

Page 14: CH 4.7 USE ISOSCELES AND EQUILATERAL TRIANGLES. In this section… We will use the facts that we know about isosceles and equilateral triangles to solve
Page 15: CH 4.7 USE ISOSCELES AND EQUILATERAL TRIANGLES. In this section… We will use the facts that we know about isosceles and equilateral triangles to solve
Page 16: CH 4.7 USE ISOSCELES AND EQUILATERAL TRIANGLES. In this section… We will use the facts that we know about isosceles and equilateral triangles to solve
Page 17: CH 4.7 USE ISOSCELES AND EQUILATERAL TRIANGLES. In this section… We will use the facts that we know about isosceles and equilateral triangles to solve
Page 18: CH 4.7 USE ISOSCELES AND EQUILATERAL TRIANGLES. In this section… We will use the facts that we know about isosceles and equilateral triangles to solve
Page 19: CH 4.7 USE ISOSCELES AND EQUILATERAL TRIANGLES. In this section… We will use the facts that we know about isosceles and equilateral triangles to solve

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