Construct a line segment which is 7 5 of any other line segment.

A line segment A B is given considering a point C on it such that A C : A B = 7 : 5 This means that the length of the line segment A C is 7 5 of the line segment A B . If we divide the line segment in five equal parts and select seven parts out of five, then this will be 7 5 of the whole line segment. We know that a line segment which is parallel to any side of a triangle divides the remaining sides of a triangle in the same ratio. Steps of construction: Draw a ray A Y making an acute angle at point A Cut four equal arcs on A Y and name them A A 1 , A 1 A 2 , A 2 A 3 , A 3 A 4 , A 4 A 5 , A 5 A 6 & A 6 A 7 and all these are equally spaced A A 1 = A 1 A 2 = A 2 A 3 = A 3 A 4 = A 4 A 5 = A 5 A 6 = A 6 A 7 Now join B with A 5 and draw a parallel line from A 7 to A 5 B , which intersects A B at C . Therefore, A C is the required line segment, because A C : A B = 7 : 5 .

Construct a line segment which is 7 5 of any other line segment.

A line segment A B is given considering a point C on it such that A C : A B = 7 : 5 This means that the length of the line segment A C is 7 5 of the line segment A B . If we divide the line segment in five equal parts and select seven parts out of five, then this will be 7 5 of the whole line segment. We know that a line segment which is parallel to any side of a triangle divides the remaining sides of a triangle in the same ratio. Steps of construction: Draw a ray A Y making an acute angle at point A Cut four equal arcs on A Y and name them A A 1 , A 1 A 2 , A 2 A 3 , A 3 A 4 , A 4 A 5 , A 5 A 6 & A 6 A 7 and all these are equally spaced A A 1 = A 1 A 2 = A 2 A 3 = A 3 A 4 = A 4 A 5 = A 5 A 6 = A 6 A 7 Now join B with A 5 and draw a parallel line from A 7 to A 5 B , which intersects A B at C . Therefore, A C is the required line segment, because A C : A B = 7 : 5 .

Construct a triangle which is similar to the given triangle A B C and whose sides are 5 3 times of the corresponding sides of the triangle A B C .

A triangle A B C is given to us. We have to construct a triangle which is similar to the given triangle and whose sides are 5 3 of the corresponding sides of the given triangle. We know that in similar triangles, corresponding angles are equal and corresponding sides are in the same ratio. Steps of construction: Draw a ray B Y from a point B making an acute angle on the other side of A . Extend B C and B A to get a ray B X & B Z respectively. Cut five equal arcs on B Y and name them B 1 , B 2 , B 3 , B 4 & B 5 and all these are equally spaced B B 1 = B 1 B 2 = B 2 B 3 = B 3 B 4 = B 4 B 5 Now join B 3 with C and draw a line parallel to B 3 C from B 5 which intersects B X at P . Now, draw a line parallel to A C from P , which intersects B Z at Q Therefore, Q B P is the required triangle.

Construct a similar triangle which is 3 5 of the given triangle.

A triangle A B C is given to us. We have to construct a triangle which is similar to the given triangle and whose sides are 3 5 of the corresponding sides of the given triangle. We know that in similar triangles, corresponding angles are equal and corresponding sides are in the same ratio. Steps of construction: Draw a ray B X from a point B making an acute angle on the other side of A . Cut five equal arcs on B X and name them B 1 , B 2 , B 3 , B 4 & B 5 and all these are equally spaced B B 1 = B 1 B 2 = B 2 B 3 = B 3 B 4 = B 4 B 5 Now join B 5 with C and draw a line parallel to B 5 C from B 3 which intersects B C at P . Now, draw a line parallel to A C from P , which intersects B A at Q Therefore, Q B P is the required triangle.

Construct two similar triangles. The first triangle should be 4 3 times the other triangle.

A triangle A B C is given to us. We have to construct a triangle which is similar to the given triangle and whose sides are 4 3 of the corresponding sides of the given triangle. We know that in similar triangles, corresponding angles are equal and corresponding sides are in the same ratio. Steps of construction: Draw a ray B X from a point B making an acute angle on the other side of A . Cut four equal arcs on B X and name them B 1 , B 2 , B 3 & B 4 and all these are equally spaced B B 1 = B 1 B 2 = B 2 B 3 = B 3 B 4 Now join B 3 with C and draw a line parallel to B 3 C from B 4 which intersects B C at D. Now, draw a line parallel to A C from D , which intersects B A at E Therefore, E B D is the required triangle.

E M B I B E

Mathematics Class - 10>Chapter 13 - Geometrical Constructions>Try These>Q 2

HARD

10th Chhattisgarh Board

IMPORTANT

Earn 100

Construct a line segment which is $\frac{7}{5}$ of any other line segment.

Important Questions on Geometrical Constructions

MEDIUM

10th Chhattisgarh Board

IMPORTANT

Mathematics Class - 10>Chapter 13 - Geometrical Constructions>Try These>Q 3

Draw a triangle

P Q R

in which

Q R = 6 c m, P Q = 5 c m & ∠ P Q R = 60 °

. Draw a triangle

A B C

similar to triangle

P Q R

, in which

A B = \frac{2}{5} P Q

.

HARD

10th Chhattisgarh Board

IMPORTANT

Mathematics Class - 10>Chapter 13 - Geometrical Constructions>Try These>Q 4

Construct a triangle which is similar to the given triangle $A B C$ and whose sides are $\frac{5}{3}$ times of the corresponding sides of the triangle $A B C$ .

HARD

10th Chhattisgarh Board

IMPORTANT

Mathematics Class - 10>Chapter 13 - Geometrical Constructions>Exercise – 2>Q 1

Construct a similar triangle which is