Question

Identify the correct statements about the medians and altitudes in triangle PQR, where PS is an altitude and PT is a median. Which of the following statements are correct?

1) RS = QS
2) PS is perpendicular to RQ
3) RT = QT
4) PT is perpendicular to RQ

Answer 1

The correct statements about the medians and altitudes in triangle PQR are: RS = QS, PS is perpendicular to RQ, RT = QT, and PT is perpendicular to RQ.

Step-by-step explanation:

The correct statements about the medians and altitudes in triangle PQR are:

1. RS = QS
2. PS is perpendicular to RQ
3. RT = QT
4. PT is perpendicular to RQ

To understand why these statements are correct, consider the definitions of medians and altitudes in a triangle. A median is a line segment that connects a vertex of a triangle to the midpoint of the opposite side, while an altitude is a line segment that connects a vertex of a triangle to the line containing the opposite side, perpendicular to that line. In triangle PQR, RS = QS because RS and QS are both altitudes from points R and Q, respectively, to the line containing side PQ. PS is perpendicular to RQ because PS is an altitude from point P to line RQ. RT = QT because RT and QT are both medians from points R and Q, respectively, to the midpoint of side PQ. PT is perpendicular to RQ because PT is an altitude from point P to line RQ.