Don claims that perpendicular lines are lines that intersect such that at least one of the angles is a right angle. whis statement below is yes or no?

a. intersecting lines allow for the creation of four angles with a common vertex (yes/no)
b. if one of the angles is a right angle, the vertical to it must also be a right angle (yes/no)
c. because linear pairs are complementary, the remaining two angles must also be right angles (yes/no)

a) intersecting lines allow for the creation of four angles with a common vertex. No

When two lines intersect in only one point, there will be created four quadrants, and in each quadrant, we will have an angle, and the vertex is the intersection point of the two lines. But we have another type of intersection, if we have two equal lines, those lines will intersect on all their points, and in this case, we will not have 4 angles.

b) if one of the angles is a right angle, the vertical to it must also be a right angle. Yes (Where the vertical refers to the one above/below)

When we have an intersection of two lines, two adjacent angles are always supplementary (So the sum of the measures of both angles will add up to 180°).

Then if one is 90°, the other is X:

90° + X = 180°

X = 180° - 90° = 90°

The other angle is also a right angle.

Then we can conclude that the vertical angle must also be a right angle.

c) Because linear pairs are complementary, the remaining two angles must also be right angles No

Here we should use the same reasoning as above, but the pairs are not complementary, they are supplementary, so this statement is wrong.

42.4

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