Applied Geometry

1. Applied Geometry Lesson 1-4 Conditional Statements & Their Converses Objective: Learn to write statements in if-then form and write the converses of the statements.

2. Conditional Statements • Conditional statement: • A statement written in the form if-then • If-then statement: • A statement written in the form if-then

3. Definitions • Hypothesis: • The part following the if in a conditional statement. • Conclusion: • The part following the then in a conditional statement.

4. Identify the Hypothesis and Conclusion • If it is Saturday, then Elisa plays soccer. • If two lines intersect, then their intersection is a point. H C H: it is Saturday C: Elisa plays soccer H: two lines intersect C: their intersection is a point

5. True or False • If it is the fourth of July, then it is a holiday. • If an animal lives in the water, then it is a fish. True False, counterexample whales are not fish

6. Conditional Statements 3 ways of writing • If, then • If you are a member of Congress, then you are a U.S. citizen. • (then), if • You are a U.S. citizen, if you are a member of Congress. • Everyday • All members of Congress are U.S.

7. Write 2 other forms of the statement. • If points are collinear, then they lie on the same line First identify the form of the original statement. The form is in if, then form So the forms we need are (then), if and everyday. Points lie on the same line, if they are collinear. (switch the subject since you can’t start a sentence with ‘they’.) Points that lie on the same line are collinear.

8. Write 2 other forms • If three points are noncollinear, then they determine a plane. Three points determine a plane, if they are noncollinear. Three noncollinear points determine a plane.

9. Write 2 other forms • All collinear points lie on the same line. If points are collinear, then they lie on the same line. Points lie on the same line, if they are collinear.

10. Write 2 other forms • If two lines are parallel, then they never intersect. Lines never intersect, if they are parallel. All parallel lines never intersect.

11. Converse • The converse of a conditional statement is formed by exchanging the hypothesis and the conclusion in the conditional. Not (then), if form!!!

12. Write the converse of the statement • If a figure is a triangle, then it has three angles. As is: H: a figure is a triangle C: it has three angles. Converse: H: a figure has three angles C: it is a triangle. If a figure has three angles, then it is a triangle.

13. Write the Converse • If you are at least 16 years old, then you can get a driver’s license. If you can get a driver’s license, then you are at least 16 years old.

14. Write the Converse • All collinear points lie on the same line. Need to write it in if, then form first then change to converse. If points are collinear, then they lie on the same line. If points lie on the same line, then they are collinear.

15. True or False? • If a figure is a square, then it has four sides. • Is the converse true? True Converse: If a figure has four sides, then it is a square. False, counterexample would be a rectangle.

16. Homework • Pg. 26 1 – 9 all, 10 – 36 E