Question 1
Question: 
Answer: Steps of Construction:
Step 1:
Draw a rough sketch as shown in figure and mark the given measurements.
Step 2:
Draw a line XY and on it cut off BC = 3.5cm.
Step 3:
Step 4:
Cut off a length BD=5.5cm on BY.
Step 5:
Join CD.
Step 6:
Draw the perpendicular bisector of CD.
Let the perpendicular bisector of CD intersect BD at A.
Step 7:
Join AC.
Then, ABC is the required triangle.
Question 2
Question: 
Answer: Steps of Construction:
Step 1:
Draw a rough sketch as shown in fig and mark the given measurements on it.
Step 2:
On line XY cut off BC=4.5cm.
Step 3:
Step 4:
On PBP| cut off BD=2.5cm.
Step 5:
Join CD.
Step 6:
Draw the perpendicular bisector of CD. Let the intersect BP at A.
Step 7:
Join AC.
Then ABC is the required triangle.
Question 3
Question: 
Answer: Steps of Construction:
Step 1:
Draw a rough sketch as shown in figure and mark the given measurements.
Step 2:
Draw a ray and on it mark PX=12cm, at
Step 3:
Let the rays PY and XZ intersect at A.
Step 4:
Let the perpendicular bisectors of AP and AX intersect PX at B and C respectively.
Step 5:
Join AB and AC.
ABC is the required triangle.
Question 4
Question: Construct a DABC such that BC=6cm, AB=6cm and the median AD=4cm.
Answer: Steps of Construction:
Step 1:
Draw a rough sketch and mark the given measurements.
Step 2:
Draw BC = 6cm.
Step 3:
Bisect BC at D.
Step 4:
With B as centre and radius equal to 6cm, draw an arc x of a circle. With D as centre and radius equal to 4cm, draw an arc y to intersect the arc x at A.
Step 5:
Join AB and AC.
ABC is the required triangle.
Question 5
Question: Construct an equilateral triangle if its altitude is 4cm.
Answer: Steps of Construction:
Step 1:
Draw a rough sketch as shown in figure.
Step 2:
Draw a line PQ and mark a point D on it anywhere.
Step 3:
Construct a perpendicular DE to PQ at D.
Step 4:
On DE cut off DA = 4cm.
Step 5:
Let AR intersect PQ at B.
Step 6:
On PQ cut off DC=DB.
Step 7:
Join AC.
Then, ABC is the required triangle.
Question 6
Question: Given a quadrilateral ABCD in which AB=6.3cm, BC=5.2cm, 
Answer: Steps of Construction:
Step 1:
Draw a rough sketch and mark in it the given measurements.
Construct the quadrilateral with the given measurements.
Step 2:
Join AC (diagonal).
Step 3:
Through D draw a line parallel to AC and intersecting BC produced at E.
Step 4:
Join AE.
Then, ABE is the required triangle.
Question 7
Question: 
Answer: Steps of Construction:
Step 1:
Draw a rough sketch as shown in the figure.
Step 2:
Draw a line l and on it cut off QR = 5cm.
Step 3:
Step 4:
Produce SQ and on it cut off QT = 2cm.
Step 5:
Join TR.
Step 6:
Draw the perpendicular bisector of TR. Let it intersect QS at P.
Step 7:
Join PR.
Then, PQR is the required triangle.
Question 8
Question: Construct a D ABC in which base BC=4.6cm and AB+CA=8.2cm 
Answer: Steps of Construction:
Step 1:
Draw a rough sketch as show in figure and mark in it the given measurements.
Step 2:
Draw a line XY and on it cut off BC = 4.6cm.
Step 3:
Step 4:
Cut off BD = 8.2cm on PB.
Step 5:
Join DC.
Step 6:
Draw the perpendicular bisector of DC. Let this intersect BD at A.
Step 7:
Join AC.
Then, ABC is the required triangle.
Question 9
Question: Construct a right triangle when one side is 3.5cm and the sum of the other side and the hypotenuse is 5.5cm.
Answer: Steps of Construction:
Step 1:
Draw a rough sketch as shown in figure and mark the given measurements on it.
Step 2:
Draw line XY and on it cut off BC = 3.5cm.
Step 3:
Step 4:
On BP, cut off BD = 5.5cm.
Step 5:
Join DC.
Step 6:
Draw the perpendicular bisector of DC. Let this intersect BD at A.
Step 7:
Join AC.
Then, ABC is the required right-angled triangle, right angled at B.
Question 10
Question: Construct a triangle ABC in which BC = 6.5cm, CA + AB = 10cm 
Answer: Steps of Construction:
Step 1:
Draw a rough sketch as shown in the figure and mark the given measurement.
Step 2:
Draw a line XY and on it cut off BC = 3.5cm.
Step 3:
Step 4:
On BP cut off BD = 10cm.
Step 5:
Join DC.
Step 6:
Draw the perpendicular bisector of DC. Let this intersect BD at A.
Step 7:
Join AC.
Then, ABC is the required triangle.
