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:
Draw triangle RST with RS = 4.5 cm, ∠RST = 40°, and ST = 5.7 cm.
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.
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.
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.
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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