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Question:

Construct the following quadrilaterals:
(i) Quadrilateral DEAR: DE=4 cm, EA=5 cm, AR=4.5 cm, ∠E=60°, ∠A=90°
(ii) Quadrilateral TRUE: TR=3.5 cm, RU=3 cm, UE=4 cm, ∠R=75°, ∠U=120°

Solution:

Construction of Quadrilateral DEAR:

  1. Draw DE: Draw a line segment DE of length 4 cm.
  2. Construct ∠E: At point E, construct an angle of 60° using a protractor.
  3. Mark point A: Along the ray of ∠E, mark a point A such that EA = 5 cm.
  4. Construct ∠A: At point A, construct an angle of 90° using a protractor.
  5. Mark point R: Along the ray of ∠A, mark a point R such that AR = 4.5 cm.
  6. Join DR: Join point D and R to complete the quadrilateral DEAR.

Construction of Quadrilateral TRUE:

  1. Draw TR: Draw a line segment TR of length 3.5 cm.
  2. Construct ∠R: At point R, construct an angle of 75° using a protractor.
  3. Mark point U: Along the ray of ∠R, mark a point U such that RU = 3 cm.
  4. Construct ∠U: At point U, construct an angle of 120° using a protractor.
  5. Mark point E: Along the ray of ∠U, mark a point E such that UE = 4 cm.
  6. Join TE: Join point T and E to complete the quadrilateral TRUE.