8 – 2: The Pythagorean Theorem Textbook pp

Lesson 2 MI/Vocab Pythagorean triple Use the Pythagorean Theorem and its converse. Standard 12.0 Students find and use measures of sides and of interior and exterior angles of triangles and polygons to classify figures and solve problems. (Key) Standard 14.0 Students prove the Pythagorean theorem. (Key) Standard 15.0 Students use the Pythagorean theorem to determine distance and find missing lengths of sides of right triangles.

Pythagorean Theorem In a right triangle, the sum of the squares of the measures of the legs equals the square of the measure of the hypotenuse. a 2 + b 2 = c 2 Click here for the Pythagorean Proof

Lesson 2 CYP2 1.A 2.B 3.C 4.D A.17 B.12.7 C.11.5 D.13.2 Find x. Round your answer to the nearest tenth.

Lesson 2 Ex3 Verify a Triangle is a Right Triangle COORDINATE GEOMETRY Verify that ΔABC is a right triangle. Use distance formula on all 3 sides then the Pythagorean theorem.

Lesson 2 Ex3 Verify a Triangle is a Right Triangle COORDINATE GEOMETRY Verify that ΔABC is a right triangle

1.A 2.B 3.C Lesson 2 CYP3 COORDINATE GEOMETRY Is ΔRST a right triangle? A.yes B.no C.cannot be determined

Lesson 2 Ex4 A. Determine whether 9, 12, and 15 are the sides of a right triangle. Then state whether they form a Pythagorean triple. Pythagorean Triples Since the measure of the longest side is 15, 15 must be c. Let a and b be 9 and 12. Pythagorean Theorem Simplify. Add.

Homework Chapter 8-2  Pg 444: #1 – 3, 6 – 26

base height 1.We start with half the red square, which has Area = ½ base x height 2.We move one vertex while maintaining the base & height, so that the area remains the same. This is called a SHEAR. 3.We rotate this triangle, which does not change its area. base height 4.We mark the base and height for this triangle. (Area of green square)+ (Area of red square)= Area of the blue square The Pythagorean Theorem:

base height 5.We now do a shear on this triangle, keeping the same area. Remember that this pink triangle is half the red square. Half the red square. (Area of green square)+ (Area of red square)= Area of the blue square The Pythagorean Theorem: 1.We start with half the red square, which has Area = ½ base x height 2.We move one vertex while maintaining the base & height, so that the area remains the same. This is called a SHEAR. 3.We rotate this triangle, which does not change its area. 4.We mark the base and height for this triangle.

(Area of green square)+ (Area of red square)= Area of the blue square The Pythagorean Theorem: 6.The other half of the red square has the same area as this pink triangle, so if we copy and rotate it, we get this. So, together these two pink triangles have the same area as the red square. 7.We now take half of the green square and transform it the same way. Half the red square. We end up with this triangle, which is half of the green square. Half the green square. 9.Together, they have they same area as the green square. So, we have shown that the red & green squares together have the same area as the blue square. Shear Rotate Shear 8.The other half of the green square would give us this.

(Area of green square)+ (Area of red square)= Area of the blue square The Pythagorean Theorem: 6.The other half of the red square has the same area as this pink triangle, so if we copy and rotate it, we get this. So, together these two pink triangles have the same area as the red square. 7.We now take half of the green square and transform it the same way. Half the red square. We end up with this triangle, which is half of the green square. Half the green square. 9.Together, they have they same area as the green square. So, we have shown that the red & green squares together have the same area as the blue square. We’ve PROVEN the Pythagorean Theorem! Shear Rotate Shear 8.The other half of the green square would give us this. WWWW eeee ’’’’ vvvv eeee P P P P rrrr oooo vvvv eeee nnnn tttt hhhh eeee PPPP yyyy tttt hhhh aaaa gggg oooo rrrr eeee aaaa nnnn TTTT hhhh eeee oooo rrrr eeee mmmm ( ( ( ( cccc llll iiii cccc kkkk t t t t oooo r r r r eeee tttt uuuu rrrr nnnn ))))