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Question 6
Draw a triangle ABC with side BC=7 cm,B=45,A=105. Then, construct a triangle whose sides are 4/3 times the corresponding sides of ΔABC.


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Solution

Sum of all side of triangle =180
A+B+C=180
C=180150=30
Steps of Construction:
Step I: BC = 7 cm is drawn.

Step II: At B, a ray is drawn making an angle of 45 with BC.
Step III: At C, a ray making an angle of 30 with BC is drawn intersecting the previous ray at A. Thus, A=105.
Step IV: A ray BX is drawn making an acute angle with BC opposite to vertex A.
Step V 4 points B1,B2,B3andB4 are marked at equal distances on BX.
Step VI: B3C is joined and B4C is made parallel to B3C.
Step VII: C'A' is made parallel CA.
Thus, A'BC' is the required triangle.
Justification:
B=45 (Common)
C=C
ΔABC ~ ΔABC by AA similarity condition. BCBC=ABAB=ACAC also,
BCBC=BB3BB4=34
AB=43AB,BC=43BCandAC=43AC


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