Constrcting Line Segment in a given ratio and Similar Triangles

Constructions
Serial order wise

### Transcript

Question 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 π΄_1, γ π΄γ_2, π΄_3, π΄_4β¦β¦. π΄_13, on AX such that γπ΄π΄γ_1=π΄_1 π΄_2=π΄_2 π΄_3β¦β¦. by drawing equal arcs Join γπ΅π΄γ_13. Since we want the ratio 5 : 8, Through point π΄_5 (m = 5), we draw a line parallel to π΄_13 π΅ by making β  AA5B = β  AA13C So, we copy β  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 β  AA13B = β  AA5C, So, for lines A13B and A5C, with AX as transversal, corresponding angles are equal β΄ A13B is parallel to A5C Now, Since A13B is parallel to A5C, γπ΄π΄γ_5/(π΄_5 π΄_13 )=π΄πΆ/πΆπ΅ (By Basic Proportionality Theorem) By construction, γπ΄π΄γ_5/(π΄_5 π΄_13 )= 5/8 Therefore, π΄πΆ/πΆπ΅= 5/8 Thus, C divides AB in the ratio 5 : 8