Hushar Mulga
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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:

  1. Draw triangle AMT with AM = 6.3 cm, ∠TAM = 50°, and AT = 5.6 cm.

  2. 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.

  3. 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.

  4. 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.

  5. 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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