Question

Points E, D, and H are the midpoints of the sides of ATUV. UV = 116, TV = 140, and HD = 116. Find HE.

a) 58
b) 72
c) 116
d) 140

Answer 1

Using the properties of midsegments, HE is half the length of TV, which is 70. There seems to be a typo since 70 isn't an option, hence the closest correct answer can be assumed to be 72.

This correct answer is b)

Step-by-step explanation:

The question involves finding the length of HE, where E, D, and H are midpoints of the sides of a quadrilateral ATUV. Given UV = 116, TV = 140, and HD = 116, by the properties of midsegments in a quadrilateral, HE is half the length of TV since E and H are midpoints of ATVU. Therefore, HE = 140/2 = 70.

However, there is no option for 70 in the choices provided, suggesting there might be a typo in the question or options. Nonetheless, the closest answer would be 72, choice b.

This correct answer is b)

Answer 2

The length of segment HE is 58, which is half of UV since E is the midpoint of side UV. The correct option is a.

Step-by-step explanation:

The question is asking to find the length of segment HE in the geometric figure, where E, D, and H are midpoints of the sides of quadrilateral ATUV and HD is given to be 116. Since D and H are midpoints, HD will be half the length of TV. Given that TV = 140, HD = 70 (half of 140). To find HE, we notice it is half of UV because E is the midpoint of UV. UV is given as 116, so HE will be half of that, which is 58. Hence, a is the correct option.