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  • Write True or False and give reasons for your answer in each of the following To construct a triangle similar to a given ABC with its sides of 7by 3 the corresponding sides of ABC draw a ray BX making acute angle with BCand X lies on the opposite

Write True or False and give reasons for your answer in each of the following:
To construct a triangle similar to a given \bigtriangleup ABC with its sides \frac{7}{3} of the corresponding sides of \bigtriangleup ABC, draw a ray BX making acute angle with BCand X lies on the opposite side of A with respect to BC. The points B1, B2, ....,B7 are located at equal distances on BX, B3 is joined to C and then a linesegment B_6{C}' is drawn parallel to B3C where {C}' lies on BC produced. Finally,line segment {A}'{C}' is drawn parallel to AC.

Answers (1)

Answer: False
Solution
According to question:-

To construct a triangle similar to a given \bigtriangleup ABC with its sides \frac{7}{3} of the corresponding sides of \bigtriangleup ABC

1. Draw a line segment BC
2. Taking B and C as centres draw two arcs of suitable radii intersecting each other at A.
3. Join BA and CA. ?ABC is the required triangle.
4. From B draw any ray BX downwards making an acute angle CBX.
5. Locate seven points B1, B2, b3, …. B7 on BX such that BB1 = B1B2 = B1B3 = B3B4 = B4B5 = B5B6 = B6B7.
6. Join B3C and from B7 draw a line B7C’ ? B3C intersecting the extended line segment BC at C’.
7. From point C’ draw C’A’ ? CA intersecting the extended line segment BA at A

But as given if we join B3C and from B6 draw a line B6C’ ? B3C intersecting the extended line segment BC at C’.

BB_{3}/BB_{6}={BC}/{{BC}'} = 3/6
{BC}/{{BC}'} = 1/2
BC:{BC}'= 1:2

Hence the sides are not in the ratio of 7:3       
So, the required triangle can not be constructed in this way.
Hence the given statement is false.

 

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