4 Mark Question

Question 14 Marks

Construct a right triangle having hypotenuse of length 5.6cm and one of whose acute angles measures 30°.

Answer

Here, $\angle\text{A}=30^\circ$ and $\angle\text{C}=90^\circ$
By angle sum property: $\angle\text{B}=60^\circ$
Steps for construction:
Step I: Draw the hypotenuse AB of length 5.6cm.
Step II: Draw $\angle\text{BAX}=30^\circ$ and $\angle\text{ABY}=60^\circ$
Step III: The ray AX and BY intersect at C.
Then, ABC is the required triangle.

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Question 24 Marks

Construct a $\triangle\text{ABC}$ in which BC = 6.2cm,$\angle\text{B}=60^\circ.$ and $\angle\text{C}=45^\circ.$

Answer

Steps for construction:
Step I: Draw BC = 6.2 cm
Step II: Draw $\angle\text{BCX}=45^\circ$
Step III: Draw $\angle\text{BCX}=60^\circ$
Step IV: The ray CX an BY intersect at A. Then, ABC is the required triangle.

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Question 34 Marks

Construct a $\triangle\text{ABC}$ in which BC = 4.8cm,$\angle\text{C}=90^\circ.$and AB = 6.3cm.

Answer

Steps for construction:
Step I: Draw BC = 4.8cm
Step II: Draw a perpendicular on C such that $\angle\text{C}$ is equal to 90°.
Step III: Draw an arc of radius 6.3cm from the centre B.
Step IV: Join AB.

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Question 44 Marks

Construct an equilateral triangle each of whose sides measures 6.2cm. Measure each of its angles.

Answer

Steps for construction:
Step I: Draw AB of length 6.2cm.
Step II: By taking the centres as A and B, draw equal arcs of 6.2cm on the same side of AB, cutting each other at C.
Step III: Join AC and BC.
When we will measure angles of triangle using protractor then we find that all angles are equal to 60°.

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Question 54 Marks

Construct a right-angled triangle one side of which measures 3.5cm and the length of whose hypotenuse is 6cm.

Answer

Steps for construction:
Step I: Draw AB = 3.5cm
Step II: Construct $\angle\text{ABX}=90^\circ$
Step III: With centre A, draw an arc of radius 6 cm cutting BX at C.
Step IV: Join AC.
Then, ABC is the required triangle.

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Question 64 Marks

Construct a $\triangle\text{ABC}$ in which BC = 4.3cm, $\angle\text{C}=45^\circ$ and AC = 6cm.

Answer

Steps for construction:
Step I: Draw AC = 6cm.
Step II: Draw $\angle\text{ACZ}=45^\circ$
Step III: With C as the centre, cut ray BZ at 4.3cm at point B.
Step IV: Join AB.Then, ABC is the required triangle.

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Question 74 Marks

Construct a $\triangle\text{ABC}$ in which BC = 7cm,$\angle\text{A}=45^\circ.$and $\angle\text{C}=75^\circ.$

Answer

By angle sum property:$\angle\text{B}=180^\circ-\angle\text{A}-\angle\text{C}$
$=180^\circ-45^\circ-75^\circ$
$=60^\circ$
Steps for construction:
Step I: Draw AB = 7cm
Step II: Draw $\angle\text{BAX}=45^\circ$
Step III: Draw $\angle\text{ABY}=60^\circ$
Step IV: The ray AX an BY intersect at C. Then, ABC is the required triangle.

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Question 84 Marks

Construct a $\triangle\text{ABC}$ in which AB = 3.8cm, $\angle\text{A}=60^\circ$ and AC = 5cm.

Answer

Steps for construction: Step I: Draw AB of length 3.8cm. Step II: Draw $\angle\text{BAZ}=60^\circ$. Step III: With the centre as A, cut ray AZ at 5cm at C. Step IV: Join BC. Then, ABC is the required triangle.

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