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.
- 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.
- 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.
- Step 7: Repeat step 6 from point A.
- 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.
Thus, you obtain a right-angled triangle ACB of the required measurements.
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