3.8

What’s the Condition?

Pg. 28Conditional Statements and Converses

3.8 – What's the Condition?___________Conditional Statements and Converses

Today you are going to explore conditional statements and rearrange them to develop a different meaning. You are also going to examine how to prove something with contradictions and counterexamples.

3.39 – CONDITIONAL STATEMENTSA conditional statement is a claim based on a condition of something happening. Proofs are an example of a conditional statement. If the given is true, then the proof must happen. Conditional statements are written in the form, "If __________, then______________." Rewrite each definition into a conditional statement.

a. Lines that are parallel have corresponding angles that are congruent.

If __________________________,

then _______________________

lines are parallel

corresponding angles are congruent

If a quadrilateral has both opposite sides parallel, then it is a parallelogram

b. Quadrilaterals with both opposite sides parallel are parallelograms.

If a polygon is a triangle, then has 3 sides

c. All triangles have three sides.

If a polygon has all sides and angles =, then it is regular

d. A polygon with all angles and sides congruent is regular.

3.40 – 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 could drive a black mustang

True

If 2 90 ,then it is a right anglem

If is obtuse,then it measures 155A

False,

obtuse and 160

False, rhombus

d. If a quadrilateral is equilateral, then it is equiangular.

False, rectangle

e. If a quadrilateral is equiangular, then it is equilateral.

3.41 - Converses

a. Maggie is working with a different diagram, shown at right. She concludes that x = y. Write her conditional statement that justifies her reasoning.

If lines are parallel, then alternate interior angles are equal

b. How are Jorge's and Maggie's statements related? How are they different?

If lines are parallel, then alternate interior angles are =

If alternate interior angles are =, then lines are parallel

Same words, but reversed

c. Conditional statements that have this relationship are called converses. Write the converse of the conditional statement:

If lines are parallel, then corresponding angles are equal.

If , thencorresponding angles are = lines are parallel

a. Is this conditional statement true?

yes

3.42 – True Statements

b. Write the converse of this arrow diagram as an arrow diagram or as a conditional statement. Is this converse true? Justify your answer.

1 2 90 ,If 1 2 then and are complementary

true

c. Now consider another true congruence conjecture: "If a quadrilateral is a rhombus, then its diagonals are perpendicular." Write its converse and decide if it is true. Justify your answer.

If a quadrilateral is a rhombus, then its diagonals are perp.

If , thenthe diagonals are perp. the quad is a rhombus

False, could be a kite

d. Write the converse of the arrow diagram below. Is this converse true? Justify your answer."If a shape is a rectangle, then the area is base times height.

"If a shape is a rectangle, then the area is base times height.

If , thenthe area is base x height the shape is a rectangle

False, could be a parallelogram

3.43 – 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.