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Standard VIII

Mathematics

Construction of a Right Triangle Whose One Side and Hypotenuse Are Given

Steps for the...

Question

Steps for the construction of a right triangle LMN in which $∠ M = 90^{\circ}$ , MN = 4 cm and LN = 6.2 cm is given below. Choose the correct order.

1. Draw a line segment XY.
2. Construct a line segment MP, sufficiently large such that $∠ N M P = 90^{\circ}$
3. With N as centre and radius 6.2 cm draw an arc, cutting MP at L, join NL.
4. Locate M and N on XY such that MN = 4 cm.

1,4,2,3

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1,4,3,2

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2,1,3,4

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2,3,1,4

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Solution

The correct option is A 1,4,2,3
Steps for the construction of a right triangle LMN in which $∠ M = 90^{\circ}$ , MN = 4 cm and LN = 6.2 cm is given below.

1. Draw a line segment XY.
2. Locate M and N on XY such that MN = 4 cm.
3. Construct a line segment MP, sufficiently large such that $∠ N M P = 90^{\circ}$
4. With N as centre and radius 6.2 cm draw an arc, cutting MP at L, join NL.

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Similar questions

Q. Steps for the construction of a triangle PQR of PQ=4cm,QR =5.2cm and

∠ Q = 60^{\circ}

below. Choose the correct order.
1.Draw a line segment which is sufficiently long using ruler
2.At Q, construct a line segment QM, sufficiently large such that

∠ M Q R = 60^{\circ}

3.Locate points Q and R on it such that QR=5.2 cm
4.With Q as centre and radius as 4cm,draw an arc cutting QM at P, join PR.

Q. Steps for the construction of a triangle ABC with sides AB = 5 cm, BC = 4.3 cm and AC = 4 cm is given below. Choose the correct order.

1. With A as centre and radius 4 cm , draw an arc
2. Draw a line segment which is sufficiently long using ruler.
3. Join AC and BC
4. With B as centre radius 4.3 cm, draw another arc cutting the previous arc at C.
5. Locate points A and B on it such that AB = 5 cm.

Q. Steps for the construction of a isosceles triangle ABC whose altitude is 4cm and vertex angle is

80^{\circ}

is given below. Choose the correct order.

1.With M as centre and radius 4cm, draw an arc cutting MP at A.
2.Construct B and C on XY such that

∠ M A B = \frac{80}{2} = 40^{\circ}

and

∠ M A C = \frac{80}{2} = 40^{\circ}

3.Take a point M on point XY, and draw a line MP

⊥

XY
4.Draw a line segment XY.

Q. Construct a triangle

A B C

, in which

A B = 5.5 c m, A C = 6.5 c m

and

∠ B A C = 75^{\circ}

.
Steps for its construction is given in a jumbled form. Identify its correct sequence.
1) At

A

, construct a line segment

A E

, sufficiently large, such that

∠ B A E = 75^{\circ}

, use protractor to measure

75^{\circ}

.
2) Draw a line segment which is sufficiently long using ruler.
3) With

A

as centre and radius

6.5 c m

, draw an arc cutting

A E

at C. Join

B C

. Hence,

A B C

is the required triangle.
4) Locate points

A

and

B

on it such that

A B = 5.5 c m

Vikas followed the steps given below to construct a triangle

Right-angled triangle LMN, with hypotenuse $L N = 8 cm$ and side $M N = 5 cm$ .

Step 1:
Draw the line segment MN of the length 5 cm.

Step 2:
Measure the angle M with your protractor. Make a mark at 90 degrees and draw a line MX from M passing through the mark.

Step 3:
Draw an arc with N as the centre and radius equal to $8 c m$ , such that it intersects MX.

Step 4:
Mark the point of intersection as L.

Step 5:
Join points L and N.

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