The lengths of the segments obtained using the relationships between similar triangles are;
8. a. 12 m
b. BF = 6.75 m
c. BC = 3.75 cm, CD = 7.5 m
What are similar triangles?; Similar triangles are triangles that have the same shape and may have different sizes with proportional corresponding side lengths.
a. The ratio of similar triangle corresponding sides are equivalent, whereby ΔAGD and ΔCED are similar, we get;
GD/AG = ED/CE
AG = 9 m
CE = 4.5 m
ED = 6 m
Therefore, GD/9 = 6/4.5
GD = 9 × 6/4.5
9 × 6/4.5 = 12
GD = 12 m
b. Segment GF is congruent to segment FE, GF ≅ FE, therefore;
GF = FE
GD = GF + FE + ED
GD = 12 m, ED = 6 m
12 = GF + FE + 6
GF + FE = 12 - 6
GF + FE = 6
FE + FE = 6
2 × FE = 6
FE = 6/2
FE = 3
FD = FE + ED
FD = 3 + 6
FD = 9 m
BF/FD = CE/ED
BF/9 = 4.5/6
BF = 9 × 4.5/6
BF = 6.75 m
c. AD/GD = BD/FD
15/12 = BD/9
BD = 9 × 15/12
BD = 11.25 m
AD/GD = CD/ED
15/12 = CD/6
CD = 6 × 15/12
CD = 7.5 m
BC = BD - CD
BC = 11.25 - 7.5
BC = 3.75 m