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Construction of a Triangle with Given Perimeter and Two Base Angles

To construct ...

Question

To construct a triangle similar to a given triangle ABC with its sides 6/5th of the corresponding sides of $Δ$ ABC. Correct order of steps of construction -
(a) Draw a ray AX inclined at certain angle with AB on opposite side of C.
(b) Starting from A, cut off six equal line segments AX $_{1}$ , X $_{1}$ X $_{2}$ , X $_{2}$ X $_{3}$ , X $_{3}$ X $_{4}$ , X $_{4}$ X $_{5}$ and X $_{5}$ X $_{6}$ on AX.
(c) Draw a line B'C' parallel to BC to intersect AC produced at C'
(d) Join X $_{5}$ B and draw a line X6B' parallel to X5B, to intersect AB produced at B'.

abcd

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Solution

The correct option is C abdc
To construct a triangle like the one given in the following question, the given steps are to be followed:
1. Draw a ray AX inclined at a certain angle with AB on opposite side of C.
2. Starting from A, cut off six equal line segments $A X_{1}, X_{1} X_{2}, X_{2} X_{3}, X_{3} X_{4}, X_{4} X_{5} a n d X_{5} X_{6}$ on $A X$ .
3. Join $X_{5} B$ and draw a line $X_{6} B^{'}$ parallel to $X_{5} B$ , to intersect $A B$ produced at $B^{'}$ .
4.Draw a line $B^{'} C^{'}$ parallel to $B C$ to intersect $A C$ produced at $C^{'}$ .

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Similar questions

Q. Question 2
State whether the following is true or false.
To construct a triangle similar to a given

Δ

ABC with its sides of

\frac{7}{3}

corresponding sides of

Δ

ABC, draw a ray BX making acute angle with BC and X lies on the opposite side of A with respect of BC. The points

B_{1}, B_{2}, . . . B_{7}

are located at equal distances on BX,

B_{3}

joined to C and then a line segment

B_{6} C

’ is drawn parallel to

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where C’ lies on BC produced . Finally line segment A’C’ is drawn parallel to AC.

Q. Question 2
State whether the following is true or false.
To construct a triangle similar to a given

Δ

ABC with its sides of

\frac{7}{3}

corresponding sides of

Δ

ABC, draw a ray BX making acute angle with BC and X lies on the opposite side of A with respect of BC. The points

B_{1}, B_{2}, . . . B_{7}

are located at equal distances on BX,

B_{3}

joined to C and then a line segment

B_{6} C

’ is drawn parallel to

B_{3} C

where C’ lies on BC produced . Finally line segment A’C’ is drawn parallel to AC.

Q. To construct a triangle similar to a given

△ A B C

with its sides

\frac{3}{7}

of the corresponding sides of

△ A B C

, first draw a ray

B X

such that

∠ C B X

is an acute angle and

X

lies on the opposite side of

A

with respect to

B C

. Then locate points

B_{1}, B_{2}, B_{3}, . . .

B X

at equal distances and next step is to join:

Q. A triangle

A B C

with

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

and

∠ 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}

) parallel to

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}

) points

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

on BX so that

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. To construct a triangle similar to a given ABC with its sides

\frac{3}{7}

of the corresponding sides of

Δ

ABC, first draw a ray BX such that

∠

CBX is an acute angle and X lies on the opposite side of A with respect to BC. Then locate points

B_{1}, B_{2}, B_{3},

... on BX at equal distances and next step is to join

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