Construct a triangle similar to - A B C in which A B-4-6 cm - B C-5-1 cm - - A-60- with scale factor 4- 5-

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Standard X

Mathematics

Incenter and Construction of Incircle in a Triangle

Construct a t...

Question

Construct a triangle similar to Δ ABC in which AB = 4.6 cm, BC = 5.1 cm, ∠A = 60° with scale factor 4 : 5.

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Solution

Given that

Construct a of given data, and then a triangle similar to it whose sides are of the corresponding sides of.

We follow the following steps to construct the given

Step of construction

Step: I- First of all we draw a line segment.

Step: II- With A as centre draw an angle.

Step: III- With B as centre and radius, draw an arc, intersecting the arc drawn in step II at C.

Step: IV- Joins BC to obtain.

Step: V- Below AB, makes an acute angle.

Step: VI- Along AX, mark off five points such that

Step: VII- Join.

Step: VIII- Since we have to construct a triangle each of whose sides is of the corresponding sides of.

So, we take four parts out of five equal parts on AX from point draw and meeting AB at B’.

Step: IX- From B’ draw and meeting AC at C’

Thus, is the required triangle, each of whose sides is of the corresponding sides of.

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Similar questions

Q. Construct a triangle similar to

△ A B C

in which

A B = 4.6 c m, B C = 5.1 c m,

(∠ A) = 60^{o}

with scale factor

4 : 5

Q. Question 5
Draw a

Δ A B C

in which AB = 5 cm , BC = 6 cm and

∠ A B C = 60^{\circ}

. Construct a triangle similar to ABC with scale factor

\frac{5}{7}

. Justify the construction.

Q. A triangle A′BC′ is constructed similar to

Δ A B C

with a scale factor

\frac{3}{4}

, then the ratio of areas of

Δ A' B C' a n d Δ A B C

will be

Question 2
Draw a right $Δ$ ABC in which BC = 12 cm AB = 5 cm and $∠ B = 90^{\circ}$ Construct a triangle similar to it and of scale factor $\frac{2}{3}$ . Is the new triangle also a right triangle?
Thinking process
Here scale factor $\frac{m}{n} = \frac{2}{3}$ i.e m < n then the triangle to be constructed smaller than the given triangle Use this concept and then construct the required triangle.

Question 3
Draw a $Δ$ ABC in which BC= 6cm, CA = 5 cm and AB= 4 cm .Construct a triangle similar to it and of scale factor = $\frac{5}{3}$ .
Thinking process
Here, scale factor = $\frac{m}{n} = \frac{5}{3}$ i.e m > n then the triangle to be construction is larger than the given through use this concept and then constant the required triangle.

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