(N/A) Steps of construction:$1$. Draw a line segment $AB$ of length $7 \,cm$ using a ruler.$2$. Draw a ray $AX$ making an acute angle with $AB$.$3$. L

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Step $2$: Draw an acute angle $\angle BAX$ at point $A$.

(N/A) Steps of construction:$1$. Draw a line segment $AB$ of length $7 \,cm$ using a ruler.$2$. Draw a ray $AX$ making an acute angle with $AB$.$3$. Locate $3 + 5 = 8$ points $A_1, A_2, A_3, A_4, A_5, A_6, A_7, A_8$ on ray $AX$ such that $AA_1 = A_1A_2 = A_2A_3 = A_3A_4 = A_4A_5 = A_5A_6 = A_6A_7 = A_7A_8$.$4$. Join the point $A_8$ to $B$.$5$. Through the point $A_3$,draw a line parallel to $A_8B$ (by making corresponding angles equal) to intersect $AB$ at point $M$.$6$. Thus,$M$ is the point on $AB$ which divides it in the ratio $3 : 5$.

Class 10 Mathematics Constructions Mix Examples - Constructions

Medium

Draw $\overline{ AB }$ of length $7 \,cm$ and obtain point $M$ on $\overline{ AB }$ such that $AM : MB = 3 : 5$. Write the steps of construction.

A
Step $1$: Draw a line segment $AB = 7 \,cm$.
B
Step $2$: Draw an acute angle $\angle BAX$ at point $A$.
C
Step $3$: Mark $3 + 5 = 8$ points on $AX$ at equal distances.
D
Step $4$: Join $A_8$ to $B$ and draw a line through $A_3$ parallel to $A_8B$ to intersect $AB$ at $M$.

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Draw $\Delta ABC$ with $AB = 5 \text{ cm}$,$BC = 6 \text{ cm}$,and $m\angle B = 90^{\circ}$. Then,construct $\Delta BPQ$ similar to $\Delta ABC$ such that its sides are $\frac{3}{2}$ times the corresponding sides of $\Delta ABC$. Write the steps of construction.

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To construct a triangle similar to a given $\triangle ABC$ with its sides $\frac{3}{7}$ of the corresponding sides of $\triangle ABC$,first draw a ray $BX$ such that $\angle CBX$ is an acute angle and $X$ lies on the opposite side of $A$ with respect to $BC$. Then locate points $B_{1}, B_{2}, B_{3}, \dots$ on $BX$ at equal distances and the next step is to join

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Draw $\overline{ XY }$ of length $11\, cm$. Draw $\odot( X, 4\, cm )$ and $\odot( Y, 3\, cm)$. From the centre of each circle,draw tangents to the other circle. Write the steps of construction.

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Draw a line segment $\overline{PQ}$ of length $8.2 \, cm$ and divide it in the ratio $3:7$ from point $P$. Write the steps of construction.

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Draw $\overline{ AB }$ of length $9\, cm$. Draw $\odot( A, 3\, cm )$ and $\odot( B, 3.5\, cm )$. From the centre of each circle,draw tangents to the other circle. Write the steps of construction.

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Draw $\overline{ AB }$ of length $7 \,cm$ and obtain point $M$ on $\overline{ AB }$ such that $AM : MB = 3 : 5$. Write the steps of construction.

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Draw $\Delta ABC$ with $AB = 5 \text{ cm}$,$BC = 6 \text{ cm}$,and $m\angle B = 90^{\circ}$. Then,construct $\Delta BPQ$ similar to $\Delta ABC$ such that its sides are $\frac{3}{2}$ times the corresponding sides of $\Delta ABC$. Write the steps of construction.

Draw $\overline{ XY }$ of length $11\, cm$. Draw $\odot( X, 4\, cm )$ and $\odot( Y, 3\, cm)$. From the centre of each circle,draw tangents to the other circle. Write the steps of construction.

Draw a line segment $\overline{PQ}$ of length $8.2 \, cm$ and divide it in the ratio $3:7$ from point $P$. Write the steps of construction.

Draw $\overline{ AB }$ of length $9\, cm$. Draw $\odot( A, 3\, cm )$ and $\odot( B, 3.5\, cm )$. From the centre of each circle,draw tangents to the other circle. Write the steps of construction.

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