Question

Which statement is an example of a transitive relationship? If x = 2y and 2y = 8, then x = 4. If ℓ ⊥ m and m ∥ n, then ℓ ⊥ n. If m ⊥ n and m ⊥ p, then m ∥​ p. If a ∥ b and b ∥ c, then a ∥ c.

Answer 1

Answer:

Last option i.e If a ∥ b and b ∥ c, then a ∥ c is correct option.

Step-by-step explanation:

Given some statements we have to choose the transitive relationship.

Transitivity property stated that if a is related to b and b is related to c then a is also related to c.

First option: If x = 2y and 2y = 8, then x = 4.

According to transitive relation  If x = 2y and 2y = 8, then x=8 but given x=4 therefore, not transitive.

Second option:  If ℓ ⊥ m and m ∥ n, then ℓ ⊥ n.

For transitive the relation between m and n must be perpendicular therefore, not transitive.

Third option:  If m ⊥ n and m ⊥ p, then m ∥​ p.

For transitive n should be perpendicular to p and then m perpendicular to p therefore, not transitive.

Fourth option:  If a ∥ b and b ∥ c, then a ∥ c.

Given a || b and b || c implies a ∥ c.

Hence, a is related to b and b is related to c then a is also related to c. Therefore, transitive relation.