HONORS GEOMETRY 8.2. The Pythagorean Theorem

Do Now: Find the missing variables. Simplify as much as possible

Homework Questions? Comments? Confusions? Concerns? ASK ASK ASK ASK!

Right Triangle Parts In a right triangle we have two legs and one hypotenuse. The hypotenuse is always across from the 90 degree angle.

Pythagorean Theorem! In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.

Why does this work?

Example One: Find x. Simplify as much as possible

Example Two: Find x. Simplify as much as possible

You Try! Find x. Simplify as much as possible.

Pythagorean Triples:

Example Three: Which Pythagorean triple?

Example Four: Which Pythagorean triple?

You Try! Which Pythagorean triple?

Example Five: A 20-foot ladder is placed against a building to reach a window that is 16 feet above the ground. How many feet away from the building is the bottom of the ladder?

You Try! A 10-foot ladder is placed against a building. The base of the ladder is 6 feet from the building. How high does the ladder reach on the building?

Do Now: Solve for the missing pieces (WT, RT, and XT)

Pythagorean Theorem Converse If the sum of the squares of the lengths of the shortest sides of a triangle is equal to the square of the length of the longest side, then the triangle is a right triangle.

Pythagorean Inequality Theorems If the square of the length of the longest side of a triangle is less than the sum of the squares of the lengths of the other two sides, then the triangle is an acute triangle.

Pythagorean Inequality Theorem If the square of the length of the longest side of a triangle is greater than the sum of the squares of the lengths of the other two sides, then the triangle is an obtuse triangle.

Example Six: Determine whether 9, 12, and 22 can be the measures of the sides of a triangle. If so, classify the triangle as acute, right, or obtuse. Justify your answer.

Example Seven: Determine whether 9, 12, and 15 can be the measures of the sides of a triangle. If so, classify the triangle as acute, right, or obtuse. Justify your answer.

Example Eight: Determine whether 10, 11, and 13 can be the measures of the sides of a triangle. If so, classify the triangle as acute, right, or obtuse. Justify your answer.

You Try! Determine whether the set of numbers 7, 8, and 14 can be the measures of the sides of a triangle. If so, classify the triangle as acute, right, or obtuse. Justify your answer. Determine whether the set of numbers 14, 18, and 33 can be the measures of the sides of a triangle. If so, classify the triangle as acute, right, or obtuse. Justify your answer.

Practice Problems Try some on your own/in your table groups. As always don’t hesitate to ask questions if you are confused!

Exit Ticket: Find x Determine whether the following three sides could be of a triangle. If so, determine what type of triangle it is: 44, 46 and 91