Pythagorean Theorem Converse
Aligned To Common Core Standard:
Grade 8 Geometry - 8.G.B.6
What Is the Converse of Pythagorean Theorem? The converse of a Pythagorean Theorem: The converse of a Pythagoras theorem is: If the square of the length of a triangle's longest side is equivalent to the sum of the length of two sides of a triangle, then that triangle is called a right-angled triangle. Proof: Just suppose that there is a triangle that is not right-angled. According to the Pythagoras theorem, BD2 = a2 + b2 + c2, hence the length of sides can be derived from given sides. Therefore, we now get an isosceles triangle ACD and ABD. It can be followed that we have congruent angles, CDA = CAD and BDA = DAB. But if the apparent inequalities contradict, BDA < CDA = CAD < DAB or DAB < CAD = CDA < BDA.
Printable Worksheets And Lessons
- Cloth Triangle Step-by-Step
Lesson - I really like the way this skill can be applied to real
world problems like this one.
- Guided Lesson -
These are all thick word problems that I would encourage students
to draw before they start on.
- Guided Lesson Explanation
- This really helps bring the theorem to light.
- Independent Practice
- A string of problems that I would start by drawing out and visualizing
- Matching Worksheet
- These are all well written problems that you will see on a test
some day soon.
- Pythagorean Theorem Worksheet Five Pack - These are the great old problems people think of as word problems. A train leaves...
- Pythagorean Theorem Worksheet Five Pack Version 2 - Half word problems and half in your face triangles.
These problems really test students to see if they truly understand the concept and use of Pythagorean theorem.
- Homework 1 - A triangle shaped piece of chocolate is 3 inches long and 5 inches wide. How long is the diagonal of triangle?
- Homework 2 - A garden is in the shape of a triangle and has sides with the lengths of 5 kilometers, 8 kilometers and 14 kilometers. Find out if it is a right triangle?
- Homework 3 - A triangular shaped field is 125 yards long and the length of the diagonal of the field is 150 yards. What is the width of the field?
It is best to diagram all of these problems so that you have a good handle on what is being asked of you.
- Practice 1 - Lauren leaves home to go to office. She drives 6 miles north and the she heads 8 miles east. How far is Lauren from her home?
- Practice 2 - Ellen leaves home to go to the playground. She drives 3 miles north and then heads 4 miles east. How far is Ellen from her home?
- Practice 3 - Todd is a window washer. He leaned a ladder against the side of a building. The top of the ladder reaches the window, which is 12 feet off the ground. The base of the ladder is 5 feet away from the building. How long is the ladder?
Math Skill Quizzes
Once again, diagramming is highly recommended for these.
- Quiz 1 - If the legs of an isosceles right triangle are 12 inches long, approximate the length of the hypotenuse to the nearest whole number.
- Quiz 2 - What is the length of the missing leg?
- Quiz 3 - Richard is riding a boat. He drives 12 m east and then heads to 20 m north. How far is he from his starting point?
How Is This Skill Used Every Day?
While we have focused much of our attention on triangles in this series of lessons and worksheets it is often difficult to see how this would be used in the real world. This skill lends itself to help determine position and relative position to another point. We use navigation apps in our everyday travels. We take for granted the math behind them. When you plug in your destination and you see that measure of how far you are away from your interest and how long it will take you to get there, this math is all behind the scenes put into action. Your device and the database that it is connected to just did this math for you by finding the length of the side of a huge helping of triangles. This skill is often used by architects and anyone trying to determine a missing length. There are so many applications of this simple concept in all forms of navigation whether you are in a car, on foot, in the air, or travelling by sea. When you look to purchase a suitcase or even a television, the concepts present in this skill are pondered to determine the right fit for us.