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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

What’s the Condition?

Pg. 28

Conditional Statements and Converses

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.

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.

lines are parallel

If __________________________,

then _______________________

corresponding angles are congruent

b. Quadrilaterals with both opposite sides parallel are parallelograms.

If a quadrilateral has both opposite sides parallel,

then it is a

parallelogram

c. All triangles have three sides. parallelograms.

then has 3 sides

If a polygon is a triangle,

If a polygon has all sides and angles =,

then it is regular

3.40 – COUNTEREXAMPLES regular.

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.

False,

you could drive a black mustang

True regular.

False, regular.

obtuse and 160

rhombus

False,

rectangle

False,

3.41 - Converses equilateral.

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 alternate interior angles are =,

then lines are parallel

If lines are parallel,

then alternate interior angles are =

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

, then

corresponding angles are =

lines are parallel

3.42 – True Statements called converses. Write the converse of the conditional statement:

a. Is this conditional statement true?

yes

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

c. Now consider another true congruence conjecture: diagram or as a conditional statement. Is this converse true? Justify your answer."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 diagonals are perp.

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

, then

the shape is a rectangle

the area is base x height

False, could be a parallelogram