Chapter 4 – Geometric Construction – Text Book Solution
Practice Set 4.1 | Q 3 | Page 96
∆AMT ~ ∆AHE. In ∆AMT, AM = 6.3 cm, ∠TAM = 50°, AT = 5.6 cm. `”AM”/”AH” = 7/5`. Construct ∆AHE.
Solution
To draw ∆AMT ~ ∆AHE with the given information, follow these steps:
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Draw triangle AMT with AM = 6.3 cm, ∠TAM = 50°, and AT = 5.6 cm.
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Draw a line segment AH, such that AM / AH = 7 / 5. To do this, measure 6.3 cm on the line segment AH and mark a point A. From point A, measure 7 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 AH.
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Draw a line segment HE parallel to line segment MT. To do this, measure the same length as MT from point A along line segment AH and mark a point D. From point D, draw a line parallel to MT, which intersects line segment HE at point E.
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Measure the lengths of the sides of triangle AHE and compare them with the corresponding sides of triangle AMT. They should be in the same ratio of 7:5 as AM to AH.
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If necessary, adjust the positions of points A, H, and E until the sides of the two triangles are in the correct ratio.
The triangles ∆AMT and ∆AHE are now constructed such that they are similar with a ratio of 7:5 and ∠TAM = ∠HEA.
Chapter 4 – Geometric Construction – Text Book Solution
Practice set 4.1 |Q 4 | P 96
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