Question 5
Draw a triangle ABC with side BC=6cm,AB=5cmand∠ABC=60∘. Then construct a triangle whose sides are 34 of the corresponding sides of the triangle ABC.
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Solution
Steps of Construction:
Step I: BC = 6 cm is drawn. Step II: At point B, AB = 5 cm is drawn making an ∠ABC=60∘ with BC. Step III: AC is joined to form ΔABC. Step IV: A ray BX is drawn making an acute angle with BC opposite to vertex A. Step V: 4 points B1 B2 B3 and B4 are marked at equal distances on BX. Step VII:B3 is joined with C' to form B3C′. Step VIII: C'A' is drawn parallel CA.
Thus, A'BC' is the required triangle. Justification: ∠A=60∘ (Common) ∠C=∠C′ ΔAB′C′ ~ ΔABC by AA similarity condition. ∴ABAB′=BCB′C′=ACAC′ also, ABAB′=AA3AA4=43 ⇒AB′=34AB,B′C′=34BCandAC′=34AC