9.1 The Theorem of Pythagoras
The Pythagorean Theorem
In a right triangle, the sum of the squares of the lengths of the ______equals the square of the length of the ______. If a andb are the lengths of the legs, and c is the length of the hypotenuse, then______.
Example 1: Find the missing length in each right triangle. Round to the nearest tenth when necessary.
a.b.
c.d.
Example 2: Find the missing length in each right triangle. Round to the nearest tenth when necessary.
a.b.
c.d.
Example 3: Use the Pythagorean Theorem to solve each problem. Round to the nearest tenth of a unit.
a. How long is a string reaching from the top of a pole 20 feet tall to a point at ground level 7 feet from
the pole?
b. How long is a string reaching from the top of a pole 7 feet tall to a point at ground level 5 feet from the
pole?
c. How long is a string reaching from the top of a pole 12 feet tall to a point at ground level 9 feet from
the pole?
Example 4: Use the Pythagorean Theorem to solve each problem. Round to the nearest tenth of a unit.
a. How high up on the wall will a 20-foot ladder touch if the ladder is placed 5 feet from the wall?
b. How high up on the wall will a 25-foot ladder touch if the ladder is placed 7 feet from the wall?
c. How high up on the wall will a 41-foot ladder touch if the ladder is placed 9 feet from the wall?
Example 5: Use the Pythagorean Theorem to solve each problem.
a. A business executive sets out from the city of Caixares and travels to the city of Velmwend,45 miles
south and 50 miles east. Upon reaching Velmwend he finds that he has forgottenhis passport, so he
sends an urgent message to his family in Caixares by homing pigeon. Ifthe pigeon travels in a straight
line back to Caixares, estimate to the nearest mile how far ithas to fly.
b. A business executive sets out from the city of Elidor and travels to the city of Peng-lai, 65 miles north
and 25 miles west. Upon reaching Peng-lai he finds that he has forgotten his passport, so he sends an
urgent message to his family in Elidor by homing pigeon. If the pigeon travels in a straight line back to
Elidor, estimate to the nearest mile how far it has to fly.
c. A business executive sets out from the city of Thornwall and travels to the city of Elidor, 50 miles
south and 95 miles east. Upon reaching Elidor he finds that he has forgotten his passport, so he sends
an urgent message to his family in Thornwall by homing pigeon. If the pigeon travels in a straight line
back to Thornwall, estimate to the nearest mile how far it has to fly.
Example 6: Find the area of a rectangular rug if the width is 12 feet and the diagonal measures 20 feet.
Example 7: An Olympic soccer field is a rectangle 100 meters long and 70 meters wide. How long is the diagonal of the field?
Example 8: What is the area of a right triangle with a leg of length 5 feet and a hypotenuse of length 13 feet?
Homework: p.465 – 466 => 1 – 16; 19; 21 – 22
Geometry Lesson 9.1: The Theorem of PhythagorasPage 1