Download Warm Up 2.1.3 Can I Reverse It?

2-23. In a conditional statement, the “if” portion of the statement is
called the hypothesis, and the “then” portion is called the conclusion. If
you reverse the order of the hypothesis and conclusion, then you have
created the converse of the statement.
a. Write the converse of the conditional statement: If
angles are vertical angles, then they are congruent.
If angles are congruent, then they are vertical angles.
b. Is the original statement true? Is the converse
true? Justify your answer.
Original is true but not converse because there are other
congruent angles that are not vertical (ex:
corresponding)
2.1.3 Can I Reverse It?
September 22, 2015
Objectives
• CO: SWBAT write the converse
relationship of conditional statements.
• LO: SWBAT investigate the relationship
between the truth of a statement and
the truth of its converse.
2-24. Every conditional statement has a converse. Consider the arrow
diagram for a familiar relationship below.
Triangles congruent → all pairs of corresponding sides are congruent.
a. In mathematics, to say that a statement is true, it must always be true. That is,
it must follow from a definition or a theorem. Is this arrow diagram true?
b. Write the converse of this arrow diagram as an arrow diagram or as a conditional
statement. Is this converse true? Justify your answer.
All pairs of corresponding sides are congruent → triangles congruent
Yes, because of SSS congruence
c. Now consider another statement below. Is this statement true?
Triangles congruent → all pairs of corresponding angles are congruent.
d. Write its converse. Is the converse true? If it is true, prove it. If it is not always
true, give a counterexample. A counterexample is a statement showing at least
one situation where a statement is false.
All pairs of corresponding angles are congruent → triangles congruent
No, because you can make a smaller triangle with the same angles
e.
Write the converse of the arrow diagram below. Is this converse true? Justify
your answer.
A polygon is a rectangle → the area of the polygon is b · h.
The area of the polygon is b · h → the polygon is a rectangle
No, because parallelograms also have the area b · h
2-25. For each statement below, rewrite it as a conditional statement or
as an arrow diagram, and state whether it is true or false. Then write
the converse of the statement and tell whether it is true or
false. Remember that for a mathematical statement to be true, it must
always be true. Justify your answers.
a. All squares are rhombuses.
If a figure is a square, then it is a rhombus.
If a figure is a rhombus, then it is a square.
b. Every isosceles triangle is equilateral.
If a triangle is isosceles, then it is equilateral.
If a triangle is equilateral, then it is isosceles.
c. Two parallel lines cut by a transversal form same-side
interior angles that are supplementary
If two parallel lines are cut by a transversal, then same-side
interior angles are supplementary.
If same-side interior angles are supplementary, then the two
lines cut by the transversal must be parallel