CONDITIONAL STATEMENTS IN GEOMETRY WORKSHEET

Problem 1 :

Rewrite the following conditional statements in if-then form.

(i) Two points are collinear if they lie on the same line.

(ii) A number is divisible by 9 is also divisible by 3.

(iii) All sharks have a boneless skeleton.

Problem 2 :

Write a counter example to show that the following conditional statement is false.

If x² = 25, then x = 5

Problem 3 :

Write the converse of the following conditional statement.

Statement :

"If two segments have the same length, then they are congruent"

Problem 4 :

Write (a) inverse, (b) converse, (c) contrapositive of the following statement.

Statement :

"If there is snow on the ground, the flowers are not in bloom"

1. Answer :

(i) If two points lie on the same line, then they are collinear.

(ii) If a number is divisible by 9, then it is divisible by 3.

(iii) If a fish is a shark, then it would have a boneless skeleton.

2. Answer :

As a counter example, let us take x = -5.

The hypothesis is true, because (-5)² = 25. But, the conclusion is false, because it is given x = 5.

It implies that the given conditional statement is false.

3. Answer :

Converse :

"If two segments are congruent, then they have the same length"

4. Answer :

(a) Inverse :

"If there is no snow on the ground, the flowers are in bloom"

(b) Converse :

"If flowers are not in bloom, then there is snow on the ground"

(b) Contrapositive :

"If flowers are in bloom, then there is no snow on the ground"

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