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Chapter 6: Q6. (page 218)

For the following conditional, write the contrapositive of the statement and find the inverse is true or false.

If 螖ABCis acute, then m鈭�C鈮�90.

Short Answer

Expert verified

The contrapositive of the conditional statement is true.

Step by step solution

01

Step 1. Apply the concept of the contrapositive of a conditional statement.

To form the inverse of the conditional statement, take the negation of both the hypothesis and the conclusion.

To form the contrapositive of the conditional statement, interchange the hypothesis and the conclusion of the inverse statement.

02

Step 2. Find the inverse of the statement.

Consider the statement 鈥渋f 螖ABCis acute, then m鈭�C鈮�90.鈥�

Write the contrapositive of this statement as follows:

Inverse: If 螖ABCis not acute then m鈭�C=90.

Contrapositive: If m鈭�C=90, then 螖ABCis not acute.

03

Step 3. Step description.

The contrapositive of the statement is 鈥淚f m鈭�C=90, then 螖ABCis not acute.鈥�

This is true, because if m鈭�C=90, then 螖ABCis right angle triangle and not an acute angle triangle.

Therefore, the contrapositive of the statement is true.

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Most popular questions from this chapter

Write an indirect proof in paragraph form.

Given: OJ炉鈮�OK炉;JE炉鈮�KE炉

Prove: OE鈫�doesn't bisect 鈭�JOK.

Write an indirect proof in paragraph form.

Given: quad. EFGH in which m鈭�EFG=93;m鈭�FGH=20; m鈭�GHE=147; m鈭�HEF=34

Prove: EFGH is not a convex quadrilateral.

Arrange sentences (a)-(e) in an order that completes an indirect proof of the following statement: In a plane, two lines perpendicular to a third line are parallel to each other.

Given: Lines a, b and t lie in a plane; a鈯�t;b鈯�t

Prove: a鈥�b

(a) Then a intersects b in some point Z.

(b) But this contradicts the theorem which says that there is exactly one line perpendicular to a given line through a point outside the line.

(c) It is false that a is not parallel to b, and it follows that a鈥�b

(d) Assume temporarily that a is not parallel to b.

(e) Then there are two lines through Z and perpendicular to t.

For the following conditional, write the inverse of the statement and find the inverse is true or false.

If 螖ABCis acute, then m鈭�C鈮�90.

Classify the following conditional as true or false.

If 鈭�BCDis an exterior angle of 螖ABC, then m鈭�BCD>m鈭�A+m鈭�B.
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