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Finding the Sum of Angles in Triangles and Quadrilaterals

Finding the Sum of Angles in Triangles and Quadrilaterals. GS5. The sum of the angles in a square. Draw a square on your slate. What is the measure of each angle in a square? Why? If each angle is 90 °, what is the sum of all four angles?

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Finding the Sum of Angles in Triangles and Quadrilaterals

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  1. Finding the Sum of Angles in Triangles and Quadrilaterals GS5

  2. The sum of the angles in a square. • Draw a square on your slate. • What is the measure of each angle in a square? Why? • If each angle is 90°, what is the sum of all four angles? • The sum of the angles in a square is always 360° because 90° x 4 = 360°. 360°

  3. What about a triangle? 45° Let’s go back to a square because we now know the sum of all four angles is 360°. Draw a square. Now divide it in half from corner to corner. What shapes do you have in each half? How big is this angle? We have cut this 90° angle in half, how big is half of 90°? This 90° angle has been cut in half as well, so how big is it? What is the sum of all three angles in the triangle? Write your answer on your slate. 90° 45° 180°

  4. The Truth about Triangles The sum of the angles in any triangle is always 180°

  5. Sum of the angles of any quadrilateral. • You can use what you know about the sum of the interior angles of a triangle to figure out the sum of the interior angles of any quadrilateral. Draw these shapes on your slate.

  6. Sum of the angles of any quadrilateral. • Divide each of the quadrilaterals into two parts from corner to corner, what is the shape that is created in each case?

  7. 180° There are two triangles in every quadrilateral, what is the sum of the angles in one of the triangles? So what is the sum of the angles of both the triangles in the quadrilateral? Write your answer on your slate. The sum of the angles of any quadrilateral is what? 360° 360°

  8. What have you learned? The sum of the angles in any triangle = 180°. The sum of the angles in any quadrilateral = 360°. Let’s add this information to your notebook. • We can use this information to solve problems.

  9. The sum of the interior angles of any triangle is 180°. • What is the measure of the missing angle in this triangle? • How can we solve this problem? ? 55° 80°

  10. Did you get . . . 45° 55° 80° 45°

  11. What is the measure of the missing angle? • The sum of the interior angles of any quadrilateral is 360°. How can we solve this problem? T = 125° 95° T 60° 80°

  12. What is the sum of the angles in a triangle? • A. It depends on the triangle. • B. 180° • C. 360° • D. 270°

  13. The sum of the angles in a quadrilateral is what? • A. 270° • B. 180° • C. 360° • D. It depends on the quadrilateral.

  14. What is the missing angle measure in this triangle? • A. 30° • B. 40° • C. 60° • D. 110° 110° ? 40°

  15. What is the missing angle measure in this quadrilateral? • A. 60° • B. 50° • C. 40° • D. 35° ? 80° 100° 130°

  16. Two angles in an isosceles triangle have a measure of 40°. What is the measure of the third angle? • A. 40° • B. 80° • C. 100° • D. 140°

  17. Freddie by Phil Bolsta I don’t like doing homework, I know that it will bore me. But now I am much happier ‘Cause Freddie does it for me! He greets me at the door each day When I come home from school. He just can’t wait to read my books – I think that’s pretty cool!

  18. 81 is an odd number! C – A – T spells cat. Chase the cat! I give him all my homework, Like history and math. And when he’s done I give him A nice warm bubble bath! My grades are so much better now, Which makes my parents glad. Freddie is the smartest dog That I have ever had!

  19. The End! Really . . . This is the end! Go do your homework!

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