Draw a line segment of length 7.6 cm and divide it in the ratio 5 : 8. Measure the two parts.
Steps of Construction :(i) Draw AB = 5.6 cm(ii) At a draw an acute ∠BAX below base AB.
(iii) On AX make 5 + 8 i.e. 13 equal parts and mark them as A1, A2, A3, A4,... A13
(iv) Join B to A13. From A5 draw A5C || A13B. C is the required point of division and AC : CB = 5 : 8.
On measuring, we getAC = 3.1 cm,CB = 4.5 cm
Justification :
Therefore,
This shows that 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.
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Last updated at July 14, 2020 by
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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