Question

PLEASE CAN SOMEONE HELP MY ASSIGNMENT!!!!!!!​

Answer 1

1. The applicable theorem is the midsegment theorem

y = 5 cm

Explanation:

The given quadrilateral MATH is an isosceles trapezoid,

The bases of the isosceles trapezoid are

b₁ =
`\overline{MA}` and b₂ =
`\overline{HT}`

The median of the isosceles trapezoid =
`\overline{LV}`

MA = 3·y - 2

HT = 2·y + 4

LV = 8.5 cm

The midsegment theorem states that the median of a trapezoid is parallel to the bases of the trapezoid and is equal to half the length of the sum of the bases of the trapezoid

The median of a trapezoid = (1/2)×(b₁ + b₂)

Therefore, we have;

The median of the isosceles trapezoid, LV, given as follows;

LV = 8.5 = (1/2)×((3·y - 2) + (2·y + 4))

LV = 8.5 = (1/2)×(5·y + 2) =

2 × 8.5 = (5·y + 2)

17 = 5·y + 2

∴ 5·y = 17 - 2 = 15

y = 15/3 = 5

y = 5 cm