127k views
2 votes
Triangle proportionality theorem

Triangle proportionality theorem-example-1

1 Answer

5 votes

SL = LD = 6.4 cm, ET = 17.06 cm, NT = 2.26 cm

To find the measures of SL, LD, ET, and NT, we can use the properties of parallel lines and similarity of triangles.

Given that LD || AE || NT, we can determine that triangles LDL' and AET are similar by AA similarity.

Let's find the corresponding sides:

LD / LA = DL' / AE. Plugging in the given measures, we have LD / 8 = 48 / 45, which gives LD = 6.4 cm.

ET / AN = DL' / AE. Plugging in the given measures, we have ET / 16 = 48 / 45, which gives ET = 17.06 cm.

NT / AN = DD' / AE. Plugging in the given measures, we have NT / 16 = 6.4 / 45, which gives NT = 2.26 cm.

Since the diagonals are parallel, we can conclude that SL = LD, which is 6.4 cm.

The probable question may be:

Given diagonals LD || AE || NT and segments measures are shown determine following measure.

IN triangle SNT, SD=48cm, SE=60cm , AE=45 cm, LA=8 cm, AN=16 cm.

Find: SL, LD, ET, NT

User Jimmy Lu
by
7.6k points