Question

1. choose the correct answer

given: △mno; segment nq is perpendicular to mo; mn = no; qo = 2.5 cm
what is the length of mq?
1.25 cm
5 cm
2.5 cm
impossible to calculate

Explanation:

Step1: Identify Triangle Type

Given \( \triangle MNO \) with \( MN = NO \), so it's isosceles with \( N \) as vertex. \( NQ \perp MO \), so \( NQ \) is altitude (and median in isosceles triangle).

Step2: Apply Median Property

In isosceles \( \triangle MNO \), altitude from \( N \) to \( MO \) (i.e., \( NQ \)) bisects \( MO \). Thus, \( MQ = QO \).

Step3: Substitute Given Value

Given \( QO = 2.5 \, \text{cm} \), so \( MQ = 2.5 \, \text{cm} \).

Answer:

2.5 cm