Question

QUESTION: AOB is a right isosceles triangle of vertex O. [OH] is the altitude relative to [AB]. P is the symmetric of H with respect to (OA).

Prove that OHAP is a square.


×i have did half of the question i still the other half, how to proof HA=PA so i xan prove it as a rhombus then to a square.PLEASE HELP I NEEEED ITT NOWWW!​

Answer 1

Explanation:

To prove that OHAP is a square, we need to show that all four sides are congruent and all four angles are right angles.

Since AOB is a right isosceles triangle, we know that angle OAB and angle OBA are both congruent to 90 degrees, which means that they are both right angles. Since [OH] is the altitude relative to [AB], it bisects angle OAB, which means that angle AOH and angle HOA are both congruent to 45 degrees. Since P is the symmetric of H with respect to OA, we know that OA is congruent to OP, and we also know that OH is congruent to OP. Therefore, all four sides of OHAP are congruent, which means that OHAP is a square.