The midpoints of an irregular quadrilateral ABCD are connected to form another quadrilateral inside ABCD. Complete the explanation of why the quadrilateral is a parallelogram.

Suppose: M, N, P, Q are the midpoints of AB, BC, CD, AD respectively

=> MNPQ is the quadrilateral inside ABCD

connect B to D, ΔABD has : M is the midpoint of AB

                                              Q is the midpoint of AD

=> MQ is the midpoint polygon of ΔABD

=> MQ // BD and MQ = 1/2.BD (1)

ΔBCD has: N is the midpoint of BC

                  P is the midpoint of DC

=> NP is the midpoint polygon of ΔBCD

=> NP // BD and NP = 1/2.BD    (2)

from (1) and (2) => MQ // NP ( //BD)

                            MQ = NP  (=1/2.BD)

=> MNPQ is a parallelogram.

=>  the quadrilateral inside ABCD is a parallelogram.

Step-by-step explanation:

answer: it is 1: 47 pm

the red lines denote the population of the bacteria after 35 hours. that would be 2,409.24. the y-intercept is the blue line which is 800 because that is the starting point. the equation used to make the graph is 800(1.032)^h, where h is the number of hours.

step-by-step explanation: