In triangles △abc and △def, m∠a=m∠e, m∠c=m∠f, ac=6, ef=2, and ab=3.3, side
df
is shorter than side
bc
by 3.2. find the unknown sides of these triangles.

BC = 4.8

DE = 1.1

DF = 1.6

Step-by-step explanation:

In ΔABC and ΔDEF

∴ m∠A = m∠E

∵ m∠C = m∠F

∴ m∠B = m∠D

∴ ΔABC similar to ΔEDF

∴ AB/ED = BC/DF = AC/EF

∵ AC = 6 and EF = 2

∵ DF = BC - 3.2

∵ AB = 3.3

∴ 3.3/ED = BC/(BC - 3.2) = 6/2

∴ ED = (3.3 × 2) ÷ 6 = 1.1

∴ 2BC = 6(BC - 3.2) ⇒ 2BC = 6BC - 19.2 ⇒ 4BC = 19.2

∴ BC = 4.8

∴ DF = 4.8 - 3.2 = 1.6

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step-by-step explanation: