Question

Construct ∆XYZ such that XY= XZ = 7.2 cm and YZ = 6.5 cm. Construct the lines of symmetry​

Answer 1

Answer:

Here, XY – XZ = 2.7 cm ∴ XY > XZ As shown in the rough figure draw seg YZ = 7.4 cm Draw a ray YP making an angle of 45° with YZ Take a point W on ray YP, such that YW = 2.7 cm. Now, XY – XW = YW [Y - W - X] ∴ XY – XW = 2.7 cm ….(i) Also, XY – XZ = 2.7 cm ….(ii) [Given] ∴ XY – XW = XY – XZ [From (i) and (ii)] ∴ XW = XZ ∴ Point X is on the perpendicular bisector of seg ZW ∴ Point X is the intersection of ray YP and the perpendicular bisector seg ZW Steps of construction: i. Draw seg YZ of length 7.4 cm. ii. Draw ray YP, such that ∠ZYP = 45°. iii. Mark point W on ray YP such that l(YW) = 2.7 cm. iv. Join points W and Z. v. Join the points X and Z. Hence, ∆XYZ is the required triangle.

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