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Construction of a Similar Triangle, When One Vertex Is Common

Δ ABC of dime...

Question

$Δ A B C$ of dimesions $A B = 4 c m, B C = 5 c m$ and ∠B= 60^ois given.
A ray $B X$ is drawn from $B$ making an acute angle with $A B$ .
5 points $B_{1}, B_{2}, B_{3}, B_{4} & B_{5}$ are located on the ray such that $B B 1 = B 1 B 2 = B 2 B 3 = B 3 B 4 = B 4 B 5$ .
$B_{4}$ is joined to $A$ and a line parallel to $B_{4} A$ is drawn through $B_{5}$ to intersect the extended line $A B$ at $A^{'}$ .
Another line is drawn through $A^{'}$ parallel to $A C$ , intersecting the extended line $B C$ at $C^{'}$ .
Find the ratio of the corresponding sides of $Δ A B C$ and $Δ A^{'} B C^{'}$ .

A

$4 : 1$

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B

$4 : 5$

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C

$1 : 4$

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D

$1 : 5$

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Solution

The correct option is B
$4 : 5$

According to the construction, $Δ B B_{4} A \sim Δ B B_{5} A^{'}$

And for similar triangles, the ratio of corresponding sides is $\frac{A B}{A^{'} B}$ .

The ratio of corresponding sides is $4 : 5$ .

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Similar questions

The ratio of corresponding sides for the pair of triangles whose construction is given as follows :
Triangle ABC of dimensions AB = 4cm, BC = 5 cm and ∠B= 60^o.
The ray BX is drawn from B making an acute angle with AB. Five points B1, B2, B3, B4 and B5 are located on the ray such that BB1 = B1B2 = B2B3 = B3B4 = B4B5.
B4 is joined to A and a line parallel to B4A is drawn through B5 to intersect the extended line AB at A'. Another line is drawn through A' parallel to AC, intersecting the extended line BC at C'.

Find the ratio of the corresponding sides of $Δ A B C$ and $Δ A^{'} B C^{'}$ .

Q. A triangle ABC with sides BC =7cm,

∠ B = 45^{\circ}, ∠ A = 105^{\circ}

is given. The image of constructing a similar triangle of

Δ A B C

whose sides are

\frac{3}{4}

times the corresponding sides of the

Δ A B C

is given below. Arrange the steps of construction in the correct order.

1.Draw any ray BX making an acute angle with BC on the side opposite to the vertex A.

2.Join

B_{4} C

and raw a line through

B_{3}

( the third point, 3 being smaller of 4 in

\frac{3}{4}

B_{4} C

to intersect BC at C'.

3.Draw a line through C' parallel to the line CA to intersect BA at A'.

4.Locate 4(the greater of 3 and 4 in

\frac{3}{4}

B_{1}, B_{2}, B_{3} and B_{4}

B B_{1} = B_{1} B_{2} = B_{2} B_{3} = B_{3} B_{4}

A B C

B C = 6 c m, A B = 5 c m

∠ A B C = 60^{\circ}

. The image of constructing a similar triangle of

Δ A B C

whose sides are

\frac{3}{4}

times the corresponding sides of the

Δ A B C

is given below.

Arrange the steps of construction in the correct order.
1. Join

B_{4} C

and raw a line through

B_{3}

(the third point, 3 being smaller of 4 in

\frac{3}{4}

B_{4} C

to intersect BC at C'.

2. Draw any ray

B X

making an acute angle with BC on the side opposite to the vertex A.

3. Locate 4 (the greater of 3 and 4 in

\frac{3}{4}

B_{1}, B_{2}, B_{3} and B_{4}

B B_{1} = B_{1} B_{2} = B_{2} B_{3} = B_{3} B_{4}

4. Draw a line through C' parallel to the line CA to intersect BA at A'.

Q. A triangle ABC with sides BC =7cm,

∠ B = 45^{\circ}, ∠ A = 105^{\circ}

is given. The image of constructing a similar triangle of

Δ A B C

whose sides are

\frac{3}{4}

times the corresponding sides of the

Δ A B C

is given below. Arrange the steps of construction in the correct order.

1.Draw any ray BX making an acute angle with BC on the side opposite to the vertex A.

2.Join

B_{4} C

and raw a line through

B_{3}

( the third point, 3 being smaller of 4 in

\frac{3}{4}

B_{4} C

to intersect BC at C'.

3.Draw a line through C' parallel to the line CA to intersect BA at A'.

4.Locate 4(the greater of 3 and 4 in

\frac{3}{4}

B_{1}, B_{2}, B_{3} and B_{4}

B B_{1} = B_{1} B_{2} = B_{2} B_{3} = B_{3} B_{4}

A B C

B C = 6 c m, A B = 5 c m

∠ A B C = 60^{\circ}

. The image of constructing a similar triangle of

Δ A B C

whose sides are

\frac{3}{4}

times the corresponding sides of the

Δ A B C

is given below.

Arrange the steps of construction in the correct order.
1. Join

B_{4} C

and raw a line through

B_{3}

(the third point, 3 being smaller of 4 in

\frac{3}{4}

B_{4} C

to intersect BC at C'.

2. Draw any ray

B X

making an acute angle with BC on the side opposite to the vertex A.

3. Locate 4 (the greater of 3 and 4 in

\frac{3}{4}

B_{1}, B_{2}, B_{3} and B_{4}

B B_{1} = B_{1} B_{2} = B_{2} B_{3} = B_{3} B_{4}

4. Draw a line through C' parallel to the line CA to intersect BA at A'.

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