Construction of a triangle with SSS criterion.Class 7

• Construction of a triangle with SSS criterion.

  • Construct a triangle ABC, given that AB = 4.5 cm, BC = 5 cm and AC = 6 cm.
    Steps:
    1. Make a rough sketch for your reference
    2. Draw a line segment BC = 5 cm
       
    3. With B as centre, draw an arc of radius 4.5 cm
       
    4. With C as centre, draw an arc of radius 6 cm and cut the previous arc
       
    5. Mark the point of intersection of arcs as A. Join AB and AC. ΔABC is now ready
       
  • Note: SSS congruency rule:-  If three sides of one triangle are equal to the corresponding three sides of another triangle, then the two triangles are congruent

• Construction of a triangle with SAS criterion

  • Construct ΔPQR with QR = 7.5 cm, PQ = 5 cm and ∠Q = 60$0^{}$.
    Steps:
    1. Make a rough sketch for your reference
    2. Draw a line segment QR = 7.5 cm
       
    3. At Q, draw QX making 60$0^{}$ with QR
       
    4. With Q as centre, draw an arc of radius 5 cm. It cuts QX at P.
       
    5. Join AB. ΔPQR is now ready
       

• Construction of a triangle with ASA criterion

  • Construct ΔXYZ with ∠X = 30$0^{}$, ∠Y = 100$0^{}$ and XY = 5.8 cm.
    Steps:
    1. Make a rough sketch for your reference
    2. Draw XY = 5.8cm
       
    3. At X, draw a ray XP making an angle of 30$0^{}$ with AB.
       
    4. At Y, draw a ray YQ making an angle of 100$0^{}$ with XY.
       
    5. The point of intersection of the two rays is Z.
    6. ΔXYZ is now completed
       

• Construction of a triangle with RHS criterion

  • Construct ΔLMN, where ∠M = 90$0^{}$, MN = 8cm and LN = 10 cm.
    Steps:
    1. Make a rough sketch for your reference
    2. Draw MN = 8 cm
       
    3. At M, draw MX ⊥ MN.
       
    4. With N as centre, draw an arc of radius 10 cm to cut MX at L
       
    5. Join LN.
    6. ΔLMN is now completed