MEDIUM
Earn 100

Draw a regular pentagon and then a triangle of the same area. 

Important Questions on Constructions

HARD
Constructing a triangle XYZ in which Y=30°, Z=90° and XY+YZ+ZX=11 cm is possible.
MEDIUM

Arrange the following steps of construction of ΔABC in which AB=5.8 cm,BC+CA=8.4 cm and B=60° in correct sequence.

Step I : Join AD.

Step II : From ray BX, cut off line segment BD=BC+CA=8.4 cm

Step III : Draw a line segment AB of length 5.8 cm.

Step IV : Draw a perpendicular bisector of AD meeting BD at point C. Join AC to obtain ABC.

Step V: Draw ABX=60° at point B of line segment AB.

EASY
Which of the following criteria can be used to draw a triangle of sides 5.3 cm, 6.4 cm, and 8 cm ?
MEDIUM
The incorrect step(s) of construction of a ABC whose perimeter is 11.6 cm and the base angles are 45° and 60° is/are
MEDIUM

Arrange the following steps of construction of a ABC in which BC=8 cm, B=60° and the difference between the other two sides is 3 cm in correct sequence.

Step I : Set off BP=3 cm.

Step II : Draw BC=8 cm.

Step III: Construct CBX=60°

Step IV: Join AC. Then, ABC is the required triangle.

Step V: Draw the right bisector of  PC, meeting PB produced at A.

Step VI: Join PC.

MEDIUM

Steps of construction of triangle ABC in which BC=8 cm, B=45° and AB-AC=1 cm are given below.

Step 1: Draw BC=8 cm.

Step 2: Construct CBX=45°

Step 3: Cut off BP=9 cm on BX. Join CP.

Step 4: Draw perpendicular bisector for PC, meeting BC produced at A.

Step 5: Join AC. Then ABC is the required triangle.

Which of the above step(s) is/are incorrect?

MEDIUM

 Can you construct ABC, in which BC=5.2 cm, C=45° and perimeter of ABC is 10 cm?

MEDIUM
With the help of a ruler and compass which of the following is not possible to draw.
MEDIUM

Arrange the following steps of construction of a PQR in which QR=5 cm,PQR=60° and QP-PR=2 cm in correct sequence.

Step I : Make an angleXQR=60° at point Q of base QR.

Step II : Join SR and draw the perpendicular bisector of SR that intersect QX at P.

Step III : Draw the base QR of length 5 cm.

Step IV : JoinPR to obtain PQR.

Step V: Cut the line segment QS=QP-PR=2 cm from the ray QX.

EASY
Which of the following is not a criterion for the construction of a triangle?
MEDIUM

Study the statements carefully and select the correct option.

Statement-I : The sum of any two sides of a triangle is always greater than the third side.

Statement-II : It is possible to construct a ABC in which AB=5 cm, BC=5 cm and AC=10 cm.

MEDIUM

Arrange the following steps of construction of a ABC, in which BC=3.8 cm,B=45° and AB+AC=6.8 cm in correct sequence.

Step I : Draw the perpendicular bisector of CD meeting BD at A.

Step II : Draw BC=3.8 cm.

Step III : Join CD.

Step IV : From ray BX, cut off line segment BD equal to AB+AC i.e, 6.8 cm.

Step V: Draw CBX=45°

Step VI: Join CA to obtain the required ABC.

EASY
The construction of a LMN in which LM=8 cm, L=45° is possible when MN+LN is
MEDIUM

A triangle, ABC, with B=70°, C=60° and AB+BC+AC=11.2 cm can be constructed.

EASY
The construction of a triangle ABC, with BC=3 cm, C=60° is possible when the difference of AB and AC is equal to
MEDIUM

Which of the following steps of construction is incorrect while constructing a ΔABC of perimeter 50 cm and B=60°,C=70°.

Step I : Draw a line segment XY equal to the perimeter (=50 cm) of ΔABC.

Step II : Construct YXD=B and XYE=C.

Step III : Draw bisectors of angles YDX and XEY and mark their intersection point as A.

Step IV : Draw the perpendicular bisectors of XA and YA meeting XY in B and C respectively.

Step V: Join AB and AC to obtain the required triangle ABC.

EASY
The construction of a ABC in which AB=6 cm, A=50° is not possible, when difference of BC and AC is equal to
EASY
The construction of a triangle ABC in which BC=6 cm,B=45° is not possible, when difference of AB and AC is equal to
MEDIUM
The construction of a triangle ABC with AB=4 cm and A=60° is not possible, when the difference of BC and AC is equal to
MEDIUM

Study the statements carefully and select the correct option.

Statement-I: It is possible to construct a triangle whose sides measure 7 cm, 5 cm and 12cm.

Statement-II : It is possible to construct an angle of 22.5° using ruler and compass only.