Question

lesson 5 practice problems 1. select all segments that could represent a corresponding height if the side m is base. a. e b. f c. g d. h e. j f. k

Explanation:

\( m \), so yes. \( j \) and \( k \): right angles with the lower base (which is \( m \) or parallel to \( m \)), so they are also perpendicular to \( m \) (since \( m \) is parallel to the lower base). So the segments that are perpendicular to \( m \) (the base) are \( e \), \( f \), \( j \), \( k \). But let's check the original problem again. Maybe the base \( m \) is a side, and the height must be perpendicular to \( m \), so:

• \( e \): perpendicular to \( m \) (yes, right angle)
• \( f \): perpendicular to \( m \) (yes, right angle at \( m \))
• \( j \): perpendicular to \( m \) (yes, right angle)
• \( k \): perpendicular to \( m \) (yes, right angle)

Wait, but maybe the figure is a parallelogram, so the height corresponding to base \( m \) is the distance between the two parallel sides (the one with \( m \) and the opposite side). So any segment perpendicular to \( m \) and between those two sides is a height. So \( e \), \( f \), \( j \), \( k \) are all heights. But let's check the options. The user's options are A. e, B. f, C. g, D. h, E. j, F. k. So the correct ones should be A, B, E, F? Wait, no, maybe \( f \) is not? Wait, no, \( f \) is from the top vertex to \( m \), perpendicular, so it's a height. \( e \) is from the left vertex to the upper base, perpendicular to \( m \), so height. \( j \) and \( k \) are also perpendicular to \( m \) (since the lower base is \( m \) or parallel, and they have right angles), so they are heights. So the answer should be A, B, E, F? Wait, but maybe I misread the diagram. Alternatively, maybe the base \( m \) is a horizontal side, and the height is the vertical segment, so \( e \), \( f \), \( j \), \( k \) are all vertical (perpendicular to \( m \)), so they are heights. So the correct options are A. e, B. f, E. j, F. k. Wait, but let's confirm the definition: In a parallelogram, the height corresponding to a base is the length of the perpendicular segment from a point on the opposite side to the base (or its extension). So for base \( m \), any segment perpendicular to \( m \) with one end on \( m \) (or the line containing \( m \)) and the other on the opposite side is a height. So \( e \): end on \( m \), end on upper side, perpendicular: height. \( f \): end on \( m \), end on upper side, perpendicular: height. \( j \): end on lower base (parallel to \( m \)), end on upper base, perpendicular: since \( m \) is parallel to the lower base, \( j \) is perpendicular to \( m \) (because it's perpendicular to the lower base, which is parallel to \( m \)), so height. \( k \): same as \( j \), perpendicular to lower base (parallel to \( m \)), so perpendicular to \( m \), height. \( g \) and \( h \) are perpendicular to \( n \) (a slant side), not \( m \), so not heights. So the correct options are A, B, E, F.

Answer:

A. e, B. f, E. j, F. k