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MWA 10 7.1 Pythagorean

MWA 10 7.1 Pythagorean

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The Pythagorean Theorem
Slide 1
Terminology:
• Right Triangle – a triangle that has a right angle
• Hypotenuse – the side of the triangle that is directly across from the right angle.
Slide 2
Labelling Parts of a Right Triangle
Angles
• are labelled with uppercase letters. ie: A, B, C
• the letter C is most commonly used to label the right angle
Slide 3
Labelling Parts of a Right Triangle
Angles
• are labelled with uppercase letters. ie: A, B, C
• the letter C is most commonly used to label the right angle
Sides
• are labelled with lowercase letters. ie: a, b, c
• the side has the same letter as the angle across from it
• the letter c is most commonly used to label the hypotenuse (which is
directly across from the right angle)
Slide 4
Pythagorean Theorem
The Pythagorean theorem states the relationship among the sides
of a right triangle. Given a right triangle ABC with right angle C, the
Pythagorean theorem states the following:
2 2 2
a b c 
Slide 5
Pythagorean Theorem
The Pythagorean theorem states the relationship among the sides
of a right triangle. Given a right triangle, the Pythagorean theorem
can also be shown as:
     
2 2 2
1 2leg leg hypotenuse 
leg1
leg2
Example 1:
Use the Pythagorean theorem to find the length of the missing
side of the triangle to the nearest tenth of a unit.
Slide 6

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MWA 10 7.1 Pythagorean

  • 1. The Pythagorean Theorem Slide 1 Terminology: • Right Triangle – a triangle that has a right angle • Hypotenuse – the side of the triangle that is directly across from the right angle.
  • 2. Slide 2 Labelling Parts of a Right Triangle Angles • are labelled with uppercase letters. ie: A, B, C • the letter C is most commonly used to label the right angle
  • 3. Slide 3 Labelling Parts of a Right Triangle Angles • are labelled with uppercase letters. ie: A, B, C • the letter C is most commonly used to label the right angle Sides • are labelled with lowercase letters. ie: a, b, c • the side has the same letter as the angle across from it • the letter c is most commonly used to label the hypotenuse (which is directly across from the right angle)
  • 4. Slide 4 Pythagorean Theorem The Pythagorean theorem states the relationship among the sides of a right triangle. Given a right triangle ABC with right angle C, the Pythagorean theorem states the following: 2 2 2 a b c 
  • 5. Slide 5 Pythagorean Theorem The Pythagorean theorem states the relationship among the sides of a right triangle. Given a right triangle, the Pythagorean theorem can also be shown as:       2 2 2 1 2leg leg hypotenuse  leg1 leg2
  • 6. Example 1: Use the Pythagorean theorem to find the length of the missing side of the triangle to the nearest tenth of a unit. Slide 6
  • 7. Example 1: Use the Pythagorean theorem to find the length of the missing side of the triangle to the nearest tenth of a unit. Slide 7 Identify the hypotenuse. Set up the formula and solve. 2 2 2 r p q      2 2 2 3.8 5.2 q      2 2 2 3.8 5.2 q  2 14.44 27.04 q  2 41.48 q 2 41.48 q 6.44q m Note: When you take a square root of a number, normally you would include  since you do not know if the answer will be positive or negative. When dealing with distance, the answer will always be positive.
  • 8. Slide 8 Example 2: Use the Pythagorean theorem to find the lengths of the missing sides of the triangles to the nearest tenth of a unit.
  • 9. Identify the hypotenuse. Set up the formula and solve. Slide 9 Example 2: Use the Pythagorean theorem to find the lengths of the missing sides of the triangles to the nearest tenth of a unit. 2 2 2 z y x      2 22 6.9 12.8z   2 47.61 163.84z   2 116.23z  2 116.23z  10.78z Reminder – lengths are always positive so the  sign is not required.
  • 10. Slide 10 Example 3: In the Old West, settlers often fashioned tents out of a piece of cloth thrown over tent poles and then secured to the ground with stakes forming an isosceles triangle. How long would the cloth have to be so that the opening of the tent was 4 meters high and 3 meters wide?
  • 11. Slide 11 Example 3: In the Old West, settlers often fashioned tents out of a piece of cloth thrown over tent poles and then secured to the ground with stakes forming an isosceles triangle. How long would the cloth have to be so that the opening of the tent was 4 meters high and 3 meters wide? Draw a diagram. 3 4 x Set up the equation. 2 2 2 leg leg hyp  2 2 2 4 3 x  2 16 9 x  2 25 x 2 25 x 5 x Calculate length of cloth. 3 + 3 55 5 + 5 + 3 + 3 = 16 m The cloth should be 16 m long.