Construct a ABC in which AB -6 cm - - A -30- and - B -60- - Construct another AB - C - similar to ABC with base AB -8 cm-

Steps of construction: (i) Draw a line segment AB=6 cm. (ii) Construct ∠ ABP=60^∘ and ∠ QAB=30^∘. (iii) Join AC and BC such that C is the intersection point ...

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Byju's Answer

Standard X

Mathematics

Locus of the Points Equidistant From Two Given Points

Construct a A...

Question

Construct a $△ A B C$ in which AB=6 cm, $∠ A = 30^{\circ}$ and $∠ B = 60^{\circ}$ .Construct another $△ A B^{'} C^{'}$ similar to $△ A B C$ with base AB'=8 cm.

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Solution

Steps of construction:

(i) Draw a line segment AB=6 cm.

(ii) Construct $∠ A B P = 60^{\circ} a n d ∠ Q A B = 30^{\circ}$ .

(iii) Join AC and BC such that C is the intersection point of BP and AQ.

Thus, $△ A B C$ is the required trianlge.

(iv) Extend AB to B',such that AB'=8 cm.

(v) Draw $B^{'} C^{'} ∥ B C$ , such that the line drawn parallel to BC meets AQ at C'.

Then, $△ A B^{'} C^{'}$ is the required triangle similar to $△ A B C$ .

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Similar questions

Q. Construct a ∆ABC in which AB = 6 cm,

∠

A = 30º and

∠

B = 60º. Construct another ∆AB'C' similar to ∆ABC with base
AB' = 8 cm. [CBSE 2015]

Q. Construct a

Δ A B C

in which AB = 6 cm,

∠ A = 30^{\circ} a n d ∠ B = 60^{\circ} .

Construct another

Δ A B^{'} C^{'} similar to Δ A B C

with base AB' = 8 cm.

Q. A

Δ A B C

with AB = 6 cm,

∠ A = 30^{\circ}

and

∠ B = 60^{\circ}

is given. Another

Δ A B^{'} C^{'}

similar to

Δ A B C

with AB' = 8 cm is constructed as shown below:

The reason why we don't construct a ray making an acute angle at A is

Q. A

Δ A B C

with AB = 6cm,

∠ A = 30^{\circ}

and

∠ B = 60^{\circ}

is given below. The image of construction of

Δ A B^{'} C^{'}

similar to

Δ A B C

with base AB' = 8cm is given below.

Arrange the steps of construction in the correct order.
1. Draw B'C' parallel to BC such that

∠ C B A = ∠ C^{'} B^{'} A .

2. Draw

Δ A B C

as per the given specification.
3. Extend AC to B'C' so that it meets B'C' at C'.
4. Extend AB to B' such that AB' = 8cm.

Q. A

Δ A B C

with AB = 6 cm,

∠ A = 30^{\circ}

and

∠ B = 60^{\circ}

is given. Another

Δ A B^{'} C^{'}

similar to

Δ A B C

with AB' = 8 cm is constructed as shown below:

The reason why we don't construct a ray making an acute angle at A is

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Construct a △ABC in which AB=6 cm,∠A=30∘ and ∠B=60∘.Construct another △AB′C′ similar to △ABC with base AB'=8 cm.

Construct a $△ A B C$ in which AB=6 cm, $∠ A = 30^{\circ}$ and $∠ B = 60^{\circ}$ .Construct another $△ A B^{'} C^{'}$ similar to $△ A B C$ with base AB'=8 cm.