Chapter 4 – Geometric Construction – Text Book Solution
Practice Set 4.1 | Q 3 | Page 96
∆RST ~ ∆XYZ. In ∆RST, RS = 4.5 cm, ∠RST = 40°, ST = 5.7 cm Construct ∆RST and ∆XYZ, such that
RS / XY = 3 / 5
S
To draw ∆RST ~ ∆XYZ with the given information, follow these steps:
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Draw triangle RST with RS = 4.5 cm, ∠RST = 40°, and ST = 5.7 cm.
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Draw a line segment XY, such that RS / XY = 3 / 5. To do this, measure 4.5 cm on XY and mark a point A. From point A, measure 3 units in one direction and mark a point B, and then measure 5 units in the other direction and mark a point C. Join points B and C to complete the line segment XY.
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Draw a line segment XZ parallel to ST. To do this, measure the same length as ST from point X along line segment XY and mark a point D. From point D, draw a line parallel to ST, which intersects line segment YZ at point Z.
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Measure the lengths of the sides of triangle XYZ and compare them with the corresponding sides of triangle RST. They should be in the same ratio of 3:5 as RS to XY.
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If necessary, adjust the positions of points X, Y, and Z until the sides of the two triangles are in the correct ratio.
The triangles ∆RST and ∆XYZ are now constructed such that they are similar with a ratio of 3:5 and ∠RST = ∠XYZ.
Chapter 4 – Geometric Construction – Text Book Solution
Practice set 4.1 |Q 3 | P 96
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