1. 7.1 Areas of Parallelograms and Triangles

2. SWBAT… To find the area of a parallelogram To find the area of a parallelogram To find the are of a triangle To find the are of a triangle

3. Investigation Page 348 Page 348

4. Formulas… The area of a rectangle is the product of its base and its height. The area of a rectangle is the product of its base and its height. The area of a parallelogram is the product of a base and the corresponding height. The area of a parallelogram is the product of a base and the corresponding height. h b b h

5. Example 1 Find the area of the parallelogram Find the area of the parallelogram 10 13 12

6. Example 2 Find the area and perimeter of RSTU Find the area and perimeter of RSTU 30 o 24 in 32 in RS T U

7. Example 3 The deVander Dutchma’s are planning to sod some of their yard. Find the number of square yards of grass needed. The deVander Dutchma’s are planning to sod some of their yard. Find the number of square yards of grass needed. 100 ft 50 ft 60 ft 150 ft 40 ft 50 ft 200 ft House and walkways garage Veggie garden

8. Area of a triangle Any parallelogram is cut by a diagonal into two congruent triangles. Any parallelogram is cut by a diagonal into two congruent triangles. Thus the area of a triangle is half the product of the base and height. Thus the area of a triangle is half the product of the base and height.

9. Example 4 Find the area of the quadrilateral ABCD if AC = 35, BF = 18 and DE = 10 Find the area of the quadrilateral ABCD if AC = 35, BF = 18 and DE = 10 A D E B C F

10. You try… Page 351 #’s 1-13 odd Page 351 #’s 1-13 odd

11. 7.2 The Pythagorean Theorem and its Converse

12. SWBAT… To use the Pythagorean theorem To use the Pythagorean theorem To sue the converse of the Pythagorean Theorem To sue the converse of the Pythagorean Theorem

13. Reminder… In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. a 2 + b 2 = c 2 a 2 + b 2 = c 2 a b c

14. You try… Find x Find x 7 x 1414

15. Real-world connection… A baseball diamond is a square with 90-ft sides. Home plate and second base are at opposite vertices of the square. About how far from home plate is second base? A baseball diamond is a square with 90-ft sides. Home plate and second base are at opposite vertices of the square. About how far from home plate is second base?

16. Pythagorean Triples A set of nonzero whole numbers a, b and c that satisfy the equation a 2 + b 2 = c 2 A set of nonzero whole numbers a, b and c that satisfy the equation a 2 + b 2 = c 2 Common triples to remember… Common triples to remember… 3,4,5 5,12,13 8,15,177,24,25

17. Converse of the Pythagorean Theorem… The sum of the squares of the measures of two sides of the triangle equals the square of the measure of the longest side, then the triangle is a right triangle. The sum of the squares of the measures of two sides of the triangle equals the square of the measure of the longest side, then the triangle is a right triangle.

18. Right triangle? Determine if the measures of these sides are the sides of a right triangle 40, 41, 48 Determine if the measures of these sides are the sides of a right triangle 40, 41, 48

19. How to determine if a triangle is right, acute or obtuse?? If c is the longest side and If c is the longest side and a 2 + b 2 < c 2, the triangle is obtuse a 2 + b 2 > c 2 the triangle is acute a 2 + b 2 > c 2 the triangle is acute a 2 + b 2 = c 2 the triangle is right a 2 + b 2 = c 2 the triangle is right

20. Classify the triangles as right, acute or obtuse… a) 4, 5, 6 b) 15, 8, 21 c) c) d) 30, 40, 50

21. Example Find x Find x 5 5 x 11 23 x | | | |

22. You try… Page 361 4 – 28 multiples of 4 Page 361 4 – 28 multiples of 4

23. Homework… Page 353 #’s 44 – 46 Page 353 #’s 44 – 46 Page 363 #’s 36 – 57 mult of 3 Page 363 #’s 36 – 57 mult of 3