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Diagram
ΔRHP ~ ΔNED, In ΔNED, NE = 7 cm. ∠D = 30°, ∠N = 20°, `"HP"/"ED" = 4/5`, then construct ΔRHP and ∆NED
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Solution
Analysis:
In ∆NED, ∠D = 30° and ∠N = 20° ......[Given]
∴ ∠E = 130° ......(ii) [Remaining angle of a triangle]
∆RHP ∼ ∆NED
∴ `"RH"/"NE" = "HP"/"ED" = "PR"/"DN"` ......[Corresponding sides of similar triangles]
∴ `"RH"/7 = 4/5` ......[Given]
∴ RH = `(4 xx 7)/5` = 5.6 cm
Also, ∠R = ∠N, ∠H = ∠E, ∠P = ∠D ......(iiii) [Corresponding angles of similar triangles]
∴ ∠R = 20°, ∠H = 130°, ∠P = 30° ......[From (i), (ii) and (iii)]
Steps of construction:
∆NED | ∆RHP | |
i. | Draw seg NE of 7 cm | Draw seg RH of 5.6 cm |
ii. | Draw a ray NA and EB such that ∠ANE = 20° and ∠BEN = 130°. | Draw a ray RC and HD such that ∠CRH = 20° and ∠DHR = 130°. |
iii. | Name the point of intersection of rays D. | Name the point of intersection of rays P. |
Concept: Division of a Line Segment
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