Right Angled Triangle: Constructions (RHS)

Construction of a right-angled triangle is possible when the Hypotenuse and one side from the remaining two sides are known to us. A right-angled triangle is a triangle which has one of its three angles equal to 90 degrees. The other two angles are acute angles. The side opposite of the right-angle is the longest side and is called the hypotenuse. The side which makes the right angle with the base is called perpendicular.

The requirements for the construction are a ruler and a compass.

Constructions of Right-angled Triangle

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 construction

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

right angled triangle construction 2

  • 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 point P and mark an arc above C.

right angled triangle construction 3

  • Step 7: Repeat step 6 from point A.

right angled triangle construction 4

  • 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 construction 5

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

To learn more about right-angle triangle and its construction, download BYJU’S-The Learning App.

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