**Math Labs with Activity – Find the Incentre of a Given Triangle**

**OBJECTIVE**

To find the incentre of a given triangle by the method of paper folding.

**Materials Required**

- A sheet of white paper
- A geometry box

**Theory**

The point of intersection of the internal bisectors of the angles of a triangle is called its incentre.

**Procedure**

**Step 1:** Draw any triangle on the sheet of white paper.

Mark its vertices as A, B and C. We shall find the incentre of ΔABC.

**Step 2:** Fold the paper along the line passing through vertex A such that the side AB falls over the side AC. Make a crease and unfold the paper. Draw a line X_{1}Y_{1} along the crease. Mark the point D where the line X_{1}Y_{1} intersects the side BC. Then, AD is the internal bisector of ∠A as shown in Figure 17.1.

**Step 3:** Fold the paper along the line passing through the vertex B such that the side BC falls over the side AB. Make a crease and unfold the paper. Draw a line X_{2}Y_{2} along the crease. Mark the point E where the line X_{2}Y_{2} intersects the side TIC. Then, BE is the internal bisector of ∠B as shown in Figure 17.2.

**Step 4:** Mark the point of intersection of the two angle bisectors as the point I.

**Result**

The point I is the incentre of the given ΔABC.

**Remarks:**

- The teacher must explain it to the students that since all the angle bisectors of a triangle meet at a point, it is sufficient to construct only two angle bisectors so as to obtain their point of intersection as the incentre.
- The incentre of each one of the triangles—acute-angled triangle, right-angled triangle and the obtuse-angled triangle—lies inside the triangle.

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