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Question (1):
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Answer:
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.
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Question (2):
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Answer:
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.
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Question (3):
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Answer:
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.
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Question (4):
Construct a DABC such that BC=6cm, AB=6cm and the median AD=4cm.
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Answer:
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.
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Question (5):
Construct an equilateral triangle if its altitude is 4cm.
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Answer:
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.
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Question (6):
Given a quadrilateral ABCD in which AB=6.3cm, BC=5.2cm, 
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Answer:
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.
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Question (7):
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Answer:
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.
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Question (8):
Construct a D ABC in which base BC=4.6cm and AB+CA=8.2cm 
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Answer:
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.
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Question (9):
Construct a right triangle when one side is 3.5cm and the sum of the other side and the hypotenuse is 5.5cm.
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Answer:
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.
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Question (10):
Construct a triangle ABC in which BC = 6.5cm, CA + AB = 10cm 
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Answer:
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.
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Question (11):
Given a quadrilateral ABCD in which AB=7cm, BC=6cm, CD=5cm, AC=8cm and BD=9cm. Construct a triangle, equal in area to this quadrilateral on AB as base.
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Answer:
Step 1:
Draw a rough sketch and mark in it the given measurements.
Step 2:
Construct quadrilateral ABCD with the given measurements.
Step 3:
Draw the diagonal BD.
Step 4:
Through C draw a line parallel to DB and intersecting AB produced at E.
Step 5:
Join DE.
Then, ADE is the required triangle.
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Question (12):
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Answer:
 Draw a line l and on it cut off BC=5cm.
 Produce YB to form a line YBY'.
 Cut off BD'=2 cm on BY'.
 Draw the perpendicular bisector of CD'. Let this bisector intersect BY at A.
 Join AC.
Then ABC is the required triangle.
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Question (13):
Construct D ABC in which BC=5cm, AB=5cm and the median BE=3cm.
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Answer:
Let ABC be the required triangle.
It is not possible to construct triangle ABC with only two side AB and BC known.
The other two triangles ABE and BEC also cannot be constructed with the given data.
Now E is the mid-point of AC.
If we draw a line DE through E and parallel to AB, then we know that 
Similarly D becomes the mid point of BC.
Step 1:
We can construct D BDE with BD=2.5cm, BE=3cm and DE=2.5cm.
Step 2:
Produce BD to C such that DC=BD=2.5cm.
Step 3:
Join CE and produce it.
Step 4:
With B as centre and radius equal to 5cm, draw an arc meeting CE produced at A.
Step 5:
Join AB.
Then, ABC is the required triangle.
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