Let point M be outside of △ABC. Point N is the reflected image of M about the midpoint of segment AB . Point K is the reflected
image of N about the midpoint of segment BC , and point K is the reflected image of L about the midpoint of segment AC . Prove that point A is the midpoint of segment ML .
1 answer:
Explanation:
Define points D, E, F as the midpoints of AB, BC, and AC, respectively. Point D is the midpoint of both AB and MN, so AMBN is a parallelogram, and side AM is parallel to and congruent with side NB.
Point E is the midpoint of both BC and NK, so BNCK is a parallelogram with side NB parallel and congruent to side CK, and by the transitive property of congruence, also to segment AM.
Point F is the midpoint of both AC and KL, so AKCL is a parallelogram with side CK parallel and congruent to side LA. By the transitive properties of congruence and of parallelism, sides AM, NB, CK, and LA are all congruent and parallel. Since AM and LA are congruent to one another and parallel, and share point A, point A must be their midpoint.
You might be interested in
Answer:
C is correct.
Step-by-step explanation:
At a picnic,
Number of adults is 3 times as number of children.
Number of women is twice as number of men.
Total number of men, women and children at the picnic be x
Let number of children be c
Let number of men be m
Let number of women be w
# Number of women is twice as number of men, w = 2m
# Number of adults is 3 times as number of children, w + m = 3c
2m + m = 3c (∴ w=2m )
c = m
Total number of men, women and children at the picnic be x
∵ c + m + w = x
m + m + 2m = x
4m = x
Number of men,
Hence, The total number of men will be