Right Angled Triangle: Constructions (RHS)

This Criteria for construction of Triangle is possible when the Hypotenuse and one side from the remaining two sides are known to us.

The requirements for the construction are a ruler and a compass. Let us construct a right-angled triangle ABC, right angled at C. Consider the length of the hypotenuse AB = 5 cm and side CA = 3 cm. The steps for construction are:

  • Step 1: Draw a horizontal line of any length and mark a point C on it.

 right angled triangle

  • Step 2: Set the compass width to 3 cm.
  • Step 3: Place the pointer head of the compass on the point C and mark an arc on both the sides of C.

 right angled triangle

  • Step 4: Mark the points as P and A where the arcs cross the line.
  • Step 5: Set the compass width to the length of the hypotenuse, that is, 5 cm.
  • Step 6: Place the pointer head of the compass on the point P and mark an arc above C.

 right angled triangle

  • Step 7: Repeat step 6 from the point A.

 right angled triangle

  • Step 8: Mark the point as B where the two arcs cross each other.
  • Step 9: Join the points B and A as well as B and C with the ruler.

 right angled triangle

Thus, you obtain a right-angled triangle ACB of the required measurements.

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Practise This Question

Ram drew a line segment AB of length 3cm and another line segment CB of length 4cm which is perpendicular to line segment AB. What is the length of the third side of the triangle?