Draw a line segment of 7.6cm and divide it in ratio 5:8 measure the two parts
Answers
Hey,
Draw a line segment AB = 7.6 cm.
Draw a ray AX which makes an acute angle with AB.
Locate 13 points (5 + 8) A1, A2, A3, …….A13 on AX so that;
AA1 = A1A2 = A2A3 = A3A4 = A4A5 = A5A6 = A6A7 = A7A8 = A8A9 = A9A10 = A10A11 = A11A12 = A12A13
geometry construction exercise solution
Join A13 to B.
Through the point A5, draw a line A5C || A13B; which intersects AB at point C.
We get; AC : CB = 5 : 8
AC = 2.92 cm and CB = 4.68 cm
Question 2: Construct a triangle of sides 4 cm, 5 cm and 6 cm and then a triangle similar to ti whose sides are 2/3 of the corresponding sides of the first triangle.
Solution: Making the triangle.
Draw a line segment AB = 4 cm
Draw an arc at 5 cm from point A.
Draw an arc at 6 cm from point B so that it intersects the previous arc.
Joint the point of intersection from A and B.
This gives the required triangle ABC.
geometry construction exercise solution
Dividing the base in 2 : 3 ratio:
Draw a ray AX at an acute angle from AB.
Plot three points on AX so that; AA1 = A1A2 = A2A3
Join A3 to B.
Draw a line from point A2 so that this line is parallel to A3B and intersects AB at point B’.
Draw a line from point B’ parallel to BC so that this line intersects AC at point C’.
Triangle AB’C’ is the required triangle.
Question 3: Construct a triangle with sides 5 cm, 6 cm and 7 cm and then another triangle whose sides are 7/5 of the corresponding sides of the first triangle.
Solution: Making the triangle
Draw a line segment AB = 5 cm
Draw an arc at 6 cm from point A.
Draw an arc at 7 cm from point B so that it intersects the previous arc.
Joint the point of intersection from A and B.
This gives the required triangle ABC.
geometry construction exercise solution
Dividing the base:
Draw a ray AX at and acute angle from AB.
Plot seven points on AX; so that AA1 = A1A2 = A2A3 = A3A4 = A4A5 = A5A6 = A6A7.
Join A5 to B.
Draw a line from point A7 parallel to A5B so that it joins AB’ (AB extended to AB’).
Draw a line B’C’ || BC.
Triangle AB’C’ is the required triangle.
Question 4: Construct and isosceles triangle whose base is 8 cm and altitude 4 cm and then another triangle whose sides are 3/2 times the corresponding sides of the isosceles triangle.
Solution: Making the triangle:
Draw a line segment AB = 8 cm.
Draw two intersecting arcs at 4 cm distance from points A and B; on either side of AB.
Join these arcs to get perpendicular bisector CD of AB. (Because altitude is the perpendicular bisector of base of isosceles triangle).
Join A and B to C to get the triangle ABC.
geometry construction exercise solution
Draw a ray DX at an acute angle from point D.
Plot 3 points on DX so that DD1 = D1D2 = D2D3.
Join D2 to point B.
Draw a line from D3 parallel to D2B so that it meets the extension of AB at B’.
Now, draw B’C’ || BC.
Draw A’C’ || AC.
Triangle A’B’C’ is the required triangle.
:)
Answer:
Given: Length of line segment 7.6 cm and ratio 5 : 8 i.e., m : n.
Step-by-step Construction:
Step 1: Draw a line segment AB of length 7.6 cm.
Step 2: Draw any ray AX, making an acute angle with AB.
Step 3: Locate 13 ( = m + n ) points on AX so that.
Step 4: Join.
⇒ AC = 2.9 cm and CB = 4.7 cm.
Figure is attached.