Pythagorean Theorem And Its Converse
In today'southward geometry lesson, you're going to acquire how to use the antipodal of the Pythagorean theorem.
Jenn, Founder Calcworkshop®, 15+ Years Experience (Licensed & Certified Instructor)
More specifically, yous're going to use it to classify triangles and decide missing side lengths.
Allow's jump in!
The Pythagorean theorem is one of the nearly famous equations, as it helps the states to chronicle the bending and sides of a right triangle.
And as we know, a correct triangle is comprised of two legs and a hypotenuse.
The hypotenuse is the longest side and is e'er opposite to the right angle.
Right Triangle Diagram
So when nosotros solve right triangles for the missing side length, all we practise is plug our given values into the formula and solve the corresponding equation.
Formula for Using the Pythagorean Theorem
Pythagorean Theorem Case
Simply did y'all know that we can decide whether or not a triangle is a right triangle, astute triangle, or birdbrained triangle?
It's truthful!
Just by examining its side lengths and using the antipodal Pythagorean theorem!
What is the Antipodal of the Pythagorean Theorem?
The theorem states that if the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.
And the corollary states, if a triangle with side lengths a, b, and c where c is the length of the longest side, we tin determine if the triangle is acute or obtuse.
We do this by comparing the sum of the squares of the legs is less than or greater than the square of the largest side, equally Varsity Tutors accurately states.
Antipodal of Pythagorean Theorem Formula
Make up one's mind if it'south Right, Acute, or Obtuse
In the video beneath, y'all are going to review the Pythagorean theorem and its backdrop, and then utilise the converse of the Pythagorean theorem to determine if a triangle is a right triangle, astute triangle, or obtuse triangle.
In addition, you'll larn a very important dominion for setting upwardly the converse equations. (Hint: Order Matters)
Video – Lesson & Examples
28 min
- Review of the Pythagorean Theorem (Examples #1-2)
- 00:04:21 – Understanding the Antipodal Pythagorean Theorem
- Exclusive Content for Member'south Only
- 00:06:47 – Classify the triangle as Right, Acute, or Obtuse (Examples #3-7)
- 00:17:38 – Employ the Pythagorean theorem to find the missing length of the polygon (Examples #8-eleven)
- Practice Issues with Step-by-Step Solutions
- Chapter Tests with Video Solutions
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Pythagorean Theorem And Its Converse,
Source: https://calcworkshop.com/triangle-trig/converse-pythagorean-theorem/
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