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Use isosceles and equilateral triangles

Learn about isosceles and equilateral triangles, find missing sides/angles using known facts. Base Angles Theorem, Converse, and angle calculations. Practice problems included.

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Use isosceles and equilateral triangles

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  1. Use isosceles and equilateral triangles CH 4.7

  2. In this section… • We will use the facts that we know about isosceles and equilateral triangles to solve for missing sides or angles.

  3. What do you know about an isosceles triangle? • There are two congruent sides in an isosceles triangle and two congruent angles.

  4. 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.

  5. Base Angles Theorem • If 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

  6. Converse to the Base Angles Theorem • If 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.

  7. Find the value of x. This is an isosceles triangle, so the 2 sides are congruent… 5x + 5 = 35 5x = 30 x = 6

  8. This is an isosceles triangle, so the 2 angles are congruent… 9x = 72 x = 8

  9. x + x + 102 = 180 2x + 102 = 180 2x = 78 x = 39

  10. The sum of the interior angles is 180… x + 7 = 55 x = 48 55 + 55 + y = 180 110 + y = 180 y = 170

  11. If this is an isosceles triangle then what are the two congruent angles x = 45 9y = 45 y = 5

  12. How would you find the values of x and y?

  13. What are all of the missing angles?

  14. Page 267, #3 – 6, 14 - 22

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