Pythagorean Theorem, Classifying triangles, Right Triangles By: 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 “C” Legs- 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°.)

…Continued Also 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 Theorem Example: Finding Hypotenuse To find the length of the hypotenuse, use the Pythagorean theorem A² +B² =C² Begin with the formula 50²+40²=C² Fill in known values 2500+1600=C² Simplify 4100=C² Solve for “C” SQRT of 4100=C 64.03=C (Round to nearest Hundredth) In 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”. A²+B²=C² is the formula. To find the lengths of the hypotenuse and legs, fill in lengths for each letter.

Checking for Understanding What is the longest side of a right triangle called? What are the Legs? What is the Pythagorean Theorem? And what is the Formula? Hypotenuse Shortest, attached to the right angle Strategy to find missing lengths of a right triangle A²+B²=C² 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 7²+8² doesn’t = 10² No, because 5²+6² doesn't = 10² Click for Answers, but try to solve before looking at answer.

How To…. Solve for the Legs, of a right triangle… To solve for the legs, you follow the same process. To solve, first set up the equation. A²+B²=C² 15²+B²=30² Place in the values that you know 225+B²=900 Solve the squares -225+B²=-225 Solve B²=775 225 cancels out, and 900-225=775 SQRT of 775=B Find Square root of 775 B= 27.8 (Rounded to nearest tenth)

Classifying Triangles: By Side There 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. Isosceles Equilateral Scalene

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°), a right triangle has one right(=90°) angle and two acute angles, and an obtuse triangle has one obtuse angle(>90°) and two acute angles. Right Triangle Acute Triangle Obtuse Triangle

Name the Triangle! Answers on next slide

ANSWERS 1) Isosceles Triangle 2) Equilateral Triangle 3) Scalene Triangle 4) Right Triangle 5) Acute Triangle 6) Obtuse Triangle

Practice and Review Hypotenuse FIND THE MISSING LENGTHS: Legs 6 ft.² What is the longest Side of a Right Triangle? What is the shortest? FIND THE MISSING LENGTHS: Hypotenuse Legs 6 ft.² 64.03 ft.² Click for Answers (One at a time)

Doing Good! 7.9 Inches 13 Centimeters 3.5 feet Solve for the missing Side Click for answers 7.9 Inches 13 Centimeters 3.5 feet

KEEP IT UP! Scalene, Right Triangle Isosceles, Acute Triangle Classify the following triangles by side and then by angle. Scalene, Right Triangle Isosceles, Acute Triangle Click 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