Given that AP¯¯¯¯¯⊥AB¯¯¯¯¯, BQ¯¯¯¯¯⊥AB¯¯¯¯¯, and AP¯¯¯¯¯≅BQ¯¯¯¯¯, which of the following proves that AO¯¯¯¯¯≅BO¯¯¯¯¯ and PO¯¯¯¯¯≅OQ¯¯¯¯¯? The figure shows two triangles O A P and O B Q with a common vertex O. Points A, O, B lie on one line. Points P, O, Q lie on one line.

An eight-sided die, which may or may not be a fair die, has four colors on it; you have been tossing the die for an hour and have recorded the color rolled for each toss. what is the probability you will roll a brown on your next toss of the die? express your answer as a simplified fraction or a decimal rounded to four decimal places.

What is the perimeter of trapezoid jklm? + units 2 + + units 9 + units 9 + + units

Atriangular field has sides of lengths 21, 39, and 41 yd. find the largest angle. (round your answer to the nearest degree.)