Question

If mq=pn, which theorem can be used to show that mpq=p?

1) Pythagorean theorem
2) Triangle inequality theorem
3) Angle bisector theorem
4) Transitive property of equality

Answer 1

The correct theorem to show that m_pq = p is the Transitive property of equality (Option 4).

Step-by-step explanation:

The Transitive property of equality is the appropriate theorem for this scenario. The given equation m_q = p_n can be expressed as m_pq = p_nq. According to the Transitive property, if a = b and b = c, then a = c. Applying this property to our equation, m_pq = p_nq, and since p_nq is equal to p, we can conclude that m_pq = p. Therefore, the Transitive property establishes the relationship between m_pq and p based on the given equality m_q = p_n.

In summary, the Transitive property of equality is a fundamental concept in mathematics that allows us to extend equality relationships. In this case, it enables us to connect the expressions m_pq and p through the given equation m_q = p_n. By understanding and applying this property, we can confidently assert that m_pq = p, providing a clear and concise solution to the mathematical question at hand.