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3.8. What’s the Condition? Pg. 28 Conditional Statements and Converses. 3.8 – What's the Condition?___________ Conditional Statements and Converses.

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3 8

3.8

What’s the Condition?

Pg. 28

Conditional Statements and Converses


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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.


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3.39 – CONDITIONAL STATEMENTS

A 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.


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

lines are parallel

If __________________________,

then _______________________

corresponding angles are congruent


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b. Quadrilaterals with both opposite sides parallel are parallelograms.

If a quadrilateral has both opposite sides parallel,

then it is a

parallelogram


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c. All triangles have three sides.

then has 3 sides

If a polygon is a triangle,


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

If a polygon has all sides and angles =,

then it is regular


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3.40 – COUNTEREXAMPLES

When 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.


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

False,

you could drive a black mustang


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True


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False,

obtuse and 160


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

rhombus

False,


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

rectangle

False,


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3.41 - Converses


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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


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

If alternate interior angles are =,

then lines are parallel

If lines are parallel,

then alternate interior angles are =

Same words, but reversed


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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

, then

corresponding angles are =

lines are parallel


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3.42 – True Statements

a. Is this conditional statement true?

yes


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

true


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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

, then

the quad is a rhombus

the diagonals are perp.

False, could be a kite


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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

, then

the shape is a rectangle

the area is base x height

False, could be a parallelogram


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3.43 – CRAZY CONVERSES

For 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!


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If you love math, then you love science

If you go to Steele Canyon, then your mascot is a cougar

If you don’t eat steak, then you are a vegetarian

If it is Halloween, then it is October 31st.


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