What is the definition or theorem if ray nm perpendicular to line gh, then angle nmp and angle pnh are complementary?
I'm not entirely sure where you have p situated, but I 'think' I know from the context of the question.
That would be one definition of complementary angles. We're told that nm is perp to gh so angle nmh is right by definition of perp. Since measure nmp + measure pnh = nmh the two are comp.
To understand the definition or theorem that states "if ray nm is perpendicular to line gh, then angle nmp and angle pnh are complementary," we need to first understand some key concepts.
1. Perpendicular lines: Two lines are considered perpendicular if they intersect at a right angle, forming four right angles at the point of intersection.
2. Complementary angles: Two angles are said to be complementary if the sum of their measures is 90 degrees. In other words, when you add the measures of two complementary angles, the result is always 90 degrees.
Now, let's examine the explanation of the given statement:
We are given that the ray nm is perpendicular to the line gh. This means that angle nmh, formed by the intersection of nm and gh, is a right angle (90 degrees) by the definition of perpendicular lines.
Now, let's consider angle nmp and angle pnh. Since nm is perpendicular to gh, nmh is a right angle. We can see that angle nmp and angle pnh share an interior angle, which is nmh. Therefore, the sum of angle nmp and angle pnh is equal to the measure of nmh, which is 90 degrees.
Hence, we can conclude that if ray nm is perpendicular to line gh, then angle nmp and angle pnh are complementary because their measures add up to 90 degrees.