In triangle PQR QM perpendicular to PR, RN perpendicular to PQR, H is ortocentre of triangle PQR then PNHM is -----
To determine the nature of quadrilateral PNHM, we can first analyze the given information and apply relevant concepts in geometry.
In triangle PQR, we know that QM is perpendicular to PR and RN is perpendicular to PQR. Additionally, we are given that H is the orthocenter of triangle PQR.
The orthocenter of a triangle is the point of intersection of its altitudes. An altitude of a triangle is a line segment drawn from a vertex perpendicular to the opposite side.
Since H is the orthocenter, we can conclude that PH is perpendicular to QR, QH is perpendicular to PR, and RH is perpendicular to PQ.
Now, let's consider the quadrilateral PNHM.
- From the information given above, we know that PH is perpendicular to QR, while QM is perpendicular to PR. This implies that PH and QM are parallel lines.
- Similarly, QH is perpendicular to PR, and RH is perpendicular to PQ. Therefore, QH and RH are also parallel lines.
When we have pairs of opposite sides that are parallel, this suggests the possibility of a parallelogram. A parallelogram is a quadrilateral with both pairs of opposite sides parallel.
In the case of PNHM, we have two pairs of opposite sides that are parallel, namely PH || QM and QH || RH. This indicates that PNHM is very likely to be a parallelogram.
However, to verify that PNHM is a parallelogram, we need to show that the opposite sides are equal in length. Without additional information about the triangle or specific measurements, we cannot conclusively determine if PNHM is a parallelogram or state any information about its side lengths.