EASY

9th Foundation

IMPORTANT

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The construction of a $∆ L M N$ in which $L M = 8 c m, ∠ L = 45 °$ is possible when $(M N + L N)$ is________.

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Important Questions on Constructions

EASY

9th Foundation

IMPORTANT

IMO Olympiad Work Book 9>Chapter 11 - Constructions>MATHEMATICAL REASONING>Q 3

Which of the following angles CANNOT be constructed by using ruler and compass only?

EASY

9th Foundation

IMPORTANT

IMO Olympiad Work Book 9>Chapter 11 - Constructions>MATHEMATICAL REASONING>Q 4

The construction of a

∆ A B C

in which

B C = 6 c m

and

∠ B = 50 °

is NOT possible when

(A B - A C)

is equal to_______.

EASY

9th Foundation

IMPORTANT

IMO Olympiad Work Book 9>Chapter 11 - Constructions>MATHEMATICAL REASONING>Q 5

Which of the following options is INCORRECT?

EASY

9th Foundation

IMPORTANT

IMO Olympiad Work Book 9>Chapter 11 - Constructions>ACHIEVERS SECTION (HOTS)>Q 6

Following are the steps of construction of a

∆ ABC

in which

AB = 5 cm, ∠ A = 30 °

and

AC - BC = 2 .5 cm

. Arrange them and select the CORRECT option.

(i)

Draw

∠ BAX = 30 °

(i i)

Draw the perpendicular bisector of

BD

which cuts

AX

C .

(i i i)

Draw

AB = 5 cm

(i v)

Join

BD

(v)

Join

BC

to obtain the required

△ ABC

(v i)

From ray

AX

, cut off line segment

AD = AC - BC = 2 .5 cm

EASY

9th Foundation

IMPORTANT

IMO Olympiad Work Book 9>Chapter 11 - Constructions>ACHIEVERS SECTION (HOTS)>Q 7

State

' T'

for true and

' F'

for false.

$(i)$ A triangle whose sides measure $8 cm, 4 cm$ and $12 cm$ can be possible.
$(ii)$ It is possible to construct an angle of $67.5 °$ using ruler and compass only.
$(iii)$ It is possible to construct a $∆ X Y Z$ in which $∠ X = 60 °, ∠ Y = 100 °$ and $∠ Z = 20 °$

$(i)$ $(ii)$ $(iii)$

$(A)$ T F T
$(B)$ F F F
$(C)$ F T T
$(D)$ T T F

EASY

9th Foundation

IMPORTANT

IMO Olympiad Work Book 9>Chapter 11 - Constructions>ACHIEVERS SECTION (HOTS)>Q 8

Let $ABC$ be a triangle in which $BC = 5 cm, ∠ B = 60 °$ and $AC + AB = 7 .5 cm .$ Given below are the steps of constructing the $△ ABC .$ Which of the following steps is INCORRECT?
Step I: Draw a line segment $BC$ of length $5 cm .$
Step II: Draw an $∠ XBC = 60 °$ at point $B$ of line segment $BC .$
Step III: Cut off $PB = 3 .5 cm$ on the ray $BX .$
Step IV: Join $PC .$ .
Step V: Draw $⊥$ bisector of $BC$ which intersect ray $BX$ at $A .$ Join $AC .$
Step VI: $△ ABC$ is the required triangle.

EASY

9th Foundation

IMPORTANT

IMO Olympiad Work Book 9>Chapter 11 - Constructions>ACHIEVERS SECTION (HOTS)>Q 9

Following are the steps of construction of a rectangle

A B C D

whose adjacent sides are of lengths

5 c m

and

3.5 c m .

Arrange them and select the CORRECT option.

(P)

Draw a line segment

B C

of length

5 c m

(Q)

With

A

as centre, draw an arc of radius

5 c m

(R)

Draw an

∠ X B C = 90 °

at point

B

of line segment

B C .

(S)

Cut a line segment

A B = 3.5 c m

\bar{B X} .

(T)

With

C

as centre, draw an arc of radius

3.5 c m

which intersects the arc at

D

(U)

Join

A D

and

C D

EASY

9th Foundation

IMPORTANT

IMO Olympiad Work Book 9>Chapter 11 - Constructions>ACHIEVERS SECTION (HOTS)>Q 10

Step

I

& Step

V

are in correct order while constructing an equilateral triangle one of whose altitudes measures

5 cm .

Which of the following options is CORRECT while arranging the remaining steps in CORRECT order?
Step I: Draw a line

XY .

(i)

From

∠ P,

set off

PA = 5 cm,

cutting

PQ

A

(i i)

From

P,

draw

PQ ⊥ XY .

(i i i)

Mark any point

P

XY .

Step V: Construct

∠ PAB = 30 °

and

∠ PAC = 30 °

, meeting

XY

B

and

C

respectively.

The construction of a ∆LMN in which LM=8cm,∠L=45° is possible when (MN+LN) is________.

Important Questions on Constructions

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The construction of a $∆ L M N$ in which $L M = 8 c m, ∠ L = 45 °$ is possible when $(M N + L N)$ is________.