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Chapter 6: Q8. (page 211)

For each statement in Ex 5-10 copy and complete a table like the one shown below.

If a triangle is scalene, then it has no congruent sides.

Short Answer

Expert verified

Statement

If ?, then ?

True/false

1. Given

鈥淚f a triangle is scalene, then it has no congruent sides鈥�.

True

2. Contrapositive

If a triangle has congruent sides, then it is not scalene.

True

3. Converse

If a triangle has no congruent sides, then it is scalene.

True

4. Inverse

鈥淚f a triangle is not scalene, then it has congruent sides鈥�.

True

Step by step solution

01

Step 1. Define contrapositive, inverse, and converse for the given statement

If the given statement is 鈥樷�橧f p then q鈥欌��, the contrapositive is 鈥樷�橧f not q then not p鈥欌赌�.

If the given statement is 鈥樷�橧f p then q鈥欌��, the converse is 鈥樷�橧f q then p鈥欌赌�.

If the given statement is 鈥樷�橧f p then q鈥欌��, the inverse is 鈥樷�橧f not p then not q鈥欌赌�.

02

Step 2. Contrapositive of the given statement

The given statement is 鈥淚f a triangle is scalene, then it has no congruent sides鈥�.

Since a scalene triangle has three different measures sides.

Therefore, the given statement: 鈥淚f a triangle is scalene, then it has no congruent sides鈥� is true.

The contrapositive of the given statement is If a triangle has congruent sides, then it is not scalene.

Thus, it is also true.

03

Step 3. Check inverse and converse of the given statement

The converse of the given statement is If a triangle has no congruent sides, then it is scalene.

Thus, it is true.

The inverse of the given statement is 鈥淚f a triangle is not scalene, then it has congruent sides鈥�.

Thus, it is true.

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