1.10-Conditional Statements

Ex 1: HYPOTHESIS AND CONCLUSIONA conditional statement is a claim based on a condition of something happening. Conditional statements are written in the form, "If __________, then______________." The hypothesis is the statement that follows the “If……..”. The conclusion follows the “, then ……”. Identify the hypothesis and conclusion of the following.

a. If you break it, then you buy it.

hypothesis conclusion

b. If you are absent from school, then you need to make up your work.

Hypothesis:You are absent from school

Conclusion:You need to make up your work

c. If a number is divisible by 2, then it is even.

Hypothesis:A number is divisible by 2

Conclusion:It is even

Ex 2: CONDITIONAL STATEMENTSRewrite each definition into a conditional statement.

a. The members on the SCHS swim team use the new pool.

If_____________________________, then _________________________

you are a member on the SCHS swim team

you use the new pool

b. Eating a snickers satisfies your hunger.

If_____________________________, then _________________________

you eat a snickersit satisfies your hunger

c. All triangles have three sides.

If_____________________________, then _________________________

a shape is a triangleit has three sides

d. Complementary angles add to 90°.

If_____________________________, then _________________________

two angles are complementary

they add to 90°

Ex 3: COUNTEREXAMPLESWhen you are dealing with a conditional statement, you must assume the first part of the statement is true. Then decide if the conclusion must happen, based on the hypothesis. Determine if the statement is true or false. If it is false, provide an example of why it is false.

a. If you drive a mustang, then it is red.

False, You drive a black mustang

b. If is obtuse, then it measures 155°

False, is obtuse and is 120°

∠A

∠A

False,

AM MB

d. If an angle is bisected, then the angle is cut in half.

True

Ex 4: COMPARE STATEMENTSExamine the two statements.

#1: If you studied, then you got an A on the test.#2: If you got an A on the test, then you studied.

a. How are the two statements related?

b. Do they mean the same thing?If-then is flipped

no

Ex 5: CONVERSESA converse flips the “If____, then____” statement. Write the converse to each of the following. Then determine if the converse is true or false. If false, provide a counterexample.

a. If two angles have the same measure, then the angle is bisected.

If ______________________, then ________________________________.

an angle is bisectedthe 2 angles have the same measure

True

b. If a shape is a pentagon, then it has five sides.

If ______________________, then ________________________________.

a shape has 5 sides

it is a pentagon

True

c. If two numbers are both odd, then their sum is even.

If ___________________________, then ___________________________.

the sum of two numbers is even

the numbers are both odd

False, 2 + 2 = 4

Ex 6: CRAZY CONVERSESFor each of these problems below, make up a conditional statement or arrow diagram that meets the stated conditions. You must use a different example each time, and none of your examples can be about math!

If you go to Steele Canyon, then your mascot is a cougarIf you don’t eat steak, then you are a vegetarianIf you love math, then you love scienceIf it is Halloween, then it is October 31st.