Draw a line segment PQ of length 5.8 cm and divide it in the ratio 5:3 measure each of the two parts

Last updated at July 14, 2020 by

This video is only available for Teachoo black users

Ex 11.1, 1 Draw a line segment length 7.6 cm and divide it in the ratio 5 : 8. Measure the two parts. Give the justification of the construction. Steps of construction: Draw line segment AB of length 7.6 cm Draw any ray AX, making an acute angle with AB. Mark 13 (= 5 + 8) points 𝐴_1, 〖 𝐴〗_2, 𝐴_3, 𝐴_4……. 𝐴_13, on AX such that 〖𝐴𝐴〗_1=𝐴_1 𝐴_2=𝐴_2 𝐴_3……. by drawing equal arcs Join 〖𝐵𝐴〗_13. Since we want the ratio 5 : 8, Through point 𝐴_5 (m = 5), we draw a line parallel to 𝐴_13 𝐵 by making ∠ AA5B = ∠ AA13C So, we copy ∠ AA13B from point A5 Note: Check how to copy an angle from Chapter 14 Class 6 Thus, AC : CB = 5 : 8. On measuring AC and BC by scale. AC = 2.9 cm & BC = 4.7 cm Justification Since ∠ AA13B = ∠ AA5C, So, for lines A13B and A5C, with AX as transversal, corresponding angles are equal ∴ A13B is parallel to A5C Now, Since A13B is parallel to A5C, 〖𝐴𝐴〗_5/(𝐴_5 𝐴_13 )=𝐴𝐶/𝐶𝐵 (By Basic Proportionality Theorem) By construction, 〖𝐴𝐴〗_5/(𝐴_5 𝐴_13 )= 5/8 Therefore, 𝐴𝐶/𝐶𝐵= 5/8 Thus, C divides AB in the ratio 5 : 8

Solution:

Draw the line segment of the given length.
Then draw another line that makes an acute angle with the given line.
Divide the line into m + n parts where m and n are the ratios given.
The basic proportionality theorem states that “If a straight line is drawn parallel to a side of a triangle, then it divides the other two sides proportionally".

Steps of construction:

Draw AB = 7.6 cm
Draw ray AX, making an acute angle with AB
Mark 13 (i.e, 5 + 8) points as A₁, A₂ ,….A₁₃ on AX such that AA₁ = A₁A₂ = A₂A₃ =...... A₁₂A₁₃
Join BA₁₃
Through A₅ (since we need 5 parts to 8 parts) draw CA₅ parallel to BA₁₃ where C lies on AB.

Now AC: CB = 5 : 8

By measurement, we find that AC = 2.9 cm and CB = 4.7 cm

Proof:

CA₅ is parallel to BA₁₃

By Basic Proportionality theorem, in ΔAA₁₃B

AC/BC = AA₅/A₅A₁₃ = 5/8 (By Construction)

Thus, C divides AB in the ratio 5:8.

☛ Check: NCERT Solutions for Class 10 Maths Chapter 11

Video Solution:

NCERT Solutions Class ₁0 Maths Chapter 11 Exercise 11.1 Question 1

Summary:

Point C divides the line segment AB of length 7.6 cm in the ratio of 5:8. By measurement, we find that AC = 2.9 cm and CB = 4.7 cm.

☛ Related Questions:

Math worksheets and
visual curriculum

Steps of Construction :

Step 1 . Draw a line segment PQ = 5.8 cm.

Step 2. Draw a ray PX, making an acute angle ∠QPX .
Step 3. Along PX, mark (5+3) =8 points A1, A2, A3, A4, A5, A6, A7 and A8 , such that
PA1 = A1A2 = A2A3 = A3A4 = A4A5 = A5A6 = A6A7 = A7A8
Step 4. Join A8Q.
Step 5. From A5, draw A5C ∥ A8Q, meeting PQ at C.
Thus, C is the point on PQ, which divides it in the ratio 5:3.

Thus, PC : CQ = 5:3

From the figure, PC = 3.6 cm
CQ = 2.2 cm