Question

What is PQ ? Enter your answer as a decimal in the box. units The figure shows what appears to be acute triangle M N O. Point P is on side N O. Double tick marks pass through segments N P and P O. Point Q is on side O M. Single tick marks pass through segments O Q and Q M. Segment P Q is drawn. The length of side M N is 14.4.

Answer 1

PQ = 7.2 Thank you for describing the triangle. If you examine the figure you described, you'll realize that triangles MNO and QPO are similar triangles, with triangle QPO being half the size of triangle MNO. You can see this because both triangles have QOP as one of their angles and line segment PO is half the length of line segment NO as evidenced by the double tick marks on each side of the bisector P. Additionally, you can see that line segment QO is half the length of line segment MO as evidenced by point Q being the bisector of MO with the single tick mark on both sides of the bisector. So the length of PQ is half of the length of MN. And 14.4/2 = 7.2