Pythagorean Theorem, Classifying triangles,Right TrianglesBy: Matthew B.And Troy L.
Right Triangles***Works only for RIGHT triangles!!Hypotenuse- The longest side of a right triangle. It is also known as CLegs- The two shortest sides of a right triangle. Known as A and B. These are attached to the right angle. Hint- A Right triangle is a triangle with a 90 degree angle. Above, are the labeled Hypotenuse and legs.
Hidden Tricks! You can use hashes to help you tell if angles are the same, or sides are the same. For example, a right triangle is signified with a square, where the 90 angle is located.Other angles are signified with curves, for example two similar angles will have the same number of curves.(The sum of the Interior angles of a triangle must be 180.)
ContinuedAlso you can use hashes to tell if the lengths of sides are the same.The sides with one hash have the same length, and the side with two is a different length.
Pythagorean TheoremIn any right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.For example, the legs are represented by A, and B. The hypotenuse is represented by the letter C.A+B=C is the formula. To find the lengths of the hypotenuse and legs, fill in lengths for each letter.Example: Finding HypotenuseTo find the length of the hypotenuse, use the Pythagorean theorem
A +B =C Begin with the formula50+40=C Fill in known values2500+1600=C Simplify4100=C Solve for CSQRT of 4100=C64.03=C (Round to nearest Hundredth)
Checking for UnderstandingWhat is the longest side of a right triangle called?
What are the Legs?
What is the Pythagorean Theorem?
And what is the Formula?
Shortest, attached to the right angle
Strategy to find missing lengths of a right triangle
Click for Answers
PRACTICE MAKES PERFECT!Can you form a right triangle with the following sets of numbers? Explain.1) 7, 8, 9
2) 5, 6, 10
No, because 7+8 doesnt = 10
No, because 5+6 doesn't = 10Click for Answers, but try to solve before looking at answer.
How To.Solve for the Legs, of a right triangleTo solve for the legs, you follow the same process.
To solve, first set up the equation.A+B=C15+B=30 Place in the values that you know 225+B=900 Solve the squares-225+B=-225 SolveB=775 225 cancels out, and 900-225=775SQRT of 775=B Find Square root of 775B= 27.8 (Rounded to nearest tenth)
Classifying Triangles: By SideThere are two ways that you can classify triangles. You can classify by sides, or by the angles.To classify Triangles by their sides, you have to look at the lengths of each side. There is an equilateral triangle, an Isosceles triangle, and there is the Scalene triangle. An equilateral triangle has 3 sides with the same length. An Isosceles Triangle Has two equal sides, and one different side. A scalene triangle is a triangle with three different side lengths. IsoscelesEquilateralScalene
Classifying Triangles: By Angle
To classify Triangles by Angles, you must know the measures of the angles. If the sum of the angles measures do not come out to be 180, then the triangle is messed up. The sum of the Interior angles of a triangle must be 180. There are three types of triangles, if you are to measure by angle. (Acute, Right and Obtuse) An acute triangle has three acute angles(90) and two acute angles.Right Triangle Acute Triangle Obtuse Triangle
Name the Triangle!Answers on next slide
Practice and ReviewWhat is the longest Side of a Right Triangle?
What is the shortest?
FIND THE MISSING LENGTHS:
6 ft.64.03 ft.Click for Answers (One at a time)HypotenuseLegs
Doing Good!Solve for the missing Side
Click for answers
7.9 Inches13 Centimeters3.5 feet
KEEP IT UP!Classify the following triangles by side and then by angle.Scalene, Right TriangleIsosceles, Acute TriangleClick for answers, one at a time)
Congrats!You now know the basics of the Pythagorean theorem, and classifying triangles! I hope you learned a lot!
Created by:Troy L. &Matthew Brown