FJ is 18 units
Step-by-step explanation:
In a triangle if a segment drawn from a point on one side to another point on another side and this segment is parallel to the third side, then
In Δ FEG
∵ Point H lies on EF
∵ Point J lies on GF
∵ HJ // EG
∴ m∠FHJ = m∠FEG ⇒ corresponding angles
∴ m∠FJH = m∠FGE ⇒ corresponding angles
In the 2 Δs FHJ and FEG
∵ m∠FHJ = m∠FEG
∵ m∠FJH = m∠FGE
∵ ∠F is a common angle in the two triangles
∴ Δ FHJ is similar to Δ FEG ⇒ AAA postulate
From similarity
∴ [tex]\frac{FH}{FE}=\frac{FJ}{FG}=\frac{HJ}{EG}[/tex]
∵ EH = 8 units
∵ HF = 12 units
∵ FE = FH + HE
∴ FE = 12 + 8 = 20 units
∵ FG = 30 units
- Substitute the lengths of FH, FE, and FG in the ratio above
to find FJ
∵ [tex]\frac{12}{20}=\frac{FJ}{30}[/tex]
- By using cross multiplication
∴ FJ × 20 = 12 × 30
∴ 20 FJ = 360
- Divide both side by 20
∴ FJ = 18 units
FJ is 18 units
Learn more;
You can learn more about triangles in brainly.com/question/4354581
#LearnwithBrainly
