12. decide whether each statement is always true, sometimes true, or never true. a. when corresponding points of an original figure and its reflection are connected, the resulting segments are all perpendicular to the line of reflection. b. when a point is reflected over a horizontal line, the y-coordinate of the point stays the same. answer both questions and explain

A. Always True

B. Never True

Step-by-step explanation:

A. We have,

The corresponding points of an original figure and its reflection are located at the same distance from the axis of reflection.

So, the axis of reflection will bisect the line joining the corresponding points perpendicularly.

Thus, the line segments are always perpendicular to the axis of reflection.

B. We know that,

The co-ordinates (x,y) lying in the first quadrant, after refection over x-axis (or the horizontal line) will become (x,-y).

So, the y-coordinate changes its sign after reflection over x-axis.

Thus, y-coordinate is never same after reflection over horizontal line.

the sum of the lengths of any two sides of a triangle is greater than the length of the third side. if you take the three sides of a triangle and add them in pairs, the sum is greater than (not equal to) the third side. if that is not true, then it is not possible to construct a triangle with the given side lengths.

step-by-step explanation: