1. LESSON 5.4 Pythagorean Theorem
OBJECTIVES:
To use the Pythagorean theorem
To solve real-life problems by using the Pythagorean theorem
To use the converse of the Pythagorean theorem

2. The Pythagorean Theorem
In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the legs.

3. Using the Pythagorean Theorem6 8 x²
= x²
100= x²

4. Find the missing leg x 3 5²
x²+ 9 = 25
x² = 16

5. Find the Area of the Triangle
What is the formula for the area of a triangle?
A = ½bh
How will we find the height?

6. Find the Area of the Triangle

7. Converse of the Pythagorean Theorem
If the square of the longest side is equal to the sum of the squares of the other sides then the triangle is a Right triangle.

8. Theorem
If c2 is less then a2 + b2, then the triangle is Acute

9. Theorem
If c2 is greater then a2 + b2, then the triangle is Obtuse

10. What type of Triangle
Sides

11. What type of Triangle
Sides

12. What type of Triangle
Sides

13. What type of Triangle
Sides

14. What type of Triangle
Sides

15. What type of Triangle
Sides

16. What type of Triangle
Sides

17. What type of Triangle
Sides

18. LESSON 5.6 Segments Divided Proportionally
OBJECTIVES:
To use proportionality theorems to calculate segment lengths
To solve real-life problems by using proportions in triangles

19. THEOREM: TRIANGLE PROPORTIONALITY THEOREM If a line parallel to one side of a triangle, intersect the other
two sides, then
_____________ ______________ ______________.
it divides the other two sides proportionally

20. THEOREM: CONVERSE OF TRIANGLE
PROPORTIONALITY THEOREM
If a line divides two sides of a triangle proportionally, then_________________ _____________________ _____________________
it is parallel to the third side.

21. EXAMPLE: Finding the length of a segment
Use the Triangle
Proportionality
Theorem to find y.
CM = ___ MB
___ = ___

22. EXAMPLE: Determining Parallel Lines
Given the diagram,
determine whether
MN || GH.
LM = ___ = ___ MG
LN = ___ = ___ NH
MN ___________ GH
because________.

23. THEOREM: COROLLARY TO TRIANGLE PROPORTIONALITY THEOREM
If three parallel lines intersect two transversals, then ______________ ______________ ______________.
they divide the sides proportionally.
a = __ b

24. EXAMPLE: Using the corollary to the Triangle Proportionality Theorem
The segments joining the sides of trapezoid RSTU are parallel to its bases. Find x and y.

25. THEOREM: TRIANGLE-ANGLE- BISECTOR THEOREM
If a ray bisects an angle
of a triangle, then it
____________________ _____________________ _____________________ _____________________
_______.
divides the opposite side into segments whose lengths are proportional to the lengths of the other two sides.
a = __; a = __
b p

26. EXAMPLE: Using the Triangle-Angle-Bisector Theorem
Find the value of x.
IG = ___ GH
___ = ___

28. AG = 6
GC = 4
CF = 4
FB = 3
AE = 5
Find BE

29. FINAL CHECKS FOR UNDERSTANDING
1. In the diagram,
PQ = 9, QR = 15, and ST = 11. What is the length of ?

30. Find x.
3. The real estate term for distance along the edge of a piece of property that touches the ocean is “ocean frontage.” Find the ocean frontage for each lot shown.
Which of these lots should be listed for the highest price?

31. Mrs. McConaughy Geometry
Homework Assignment:
Mrs. McConaughy Geometry