The orthocentre is the point of concurrency of the altitudes of a triangle. Usually it is denoted by H.

**Construction of Orthocentre of a Triangle**

**Orthocentre**

The orthocentre
is the point of concurrency of the altitudes of a triangle. Usually it is denoted
by H.

**Activity 9**

**Objective** To construct a perpendicular to a line
segment from an external point using paper folding.

**Procedure** Draw a line segment *AB* and mark
an external point *P*. Move *B* along *BA* till the fold passes through
*P* and crease it along that line. The crease thus formed is the perpendicular
to *AB* through the external point *P*.

**Activity 10**

**Objective** To locate the Orthocentre of a triangle
using paper folding.

**Procedure** Using the above Activity with any two
vertices of the triangle as external points, construct the perpendiculars to opposite
sides. The point of intersection of the perpendiculars is the Orthocentre of the
given triangle.

**Example 4.13**

Construct Δ*PQR *whose sides are* PQ *= 6 cm* *∠*Q *= 600* *and* QR
*= 7* cm *and locate its Orthocentre.

*Solution*

**Step 1 **Draw the Δ*PQR* with the given measurements.

**Step 2:**

Construct
altitudes from any two vertices (say) *R* and *P*, to their opposite sides
*PQ *and* QR *respectively.

The point
of intersection of the altitude H is the Orthocentre of the given Δ*PQR*.

**Note**

Where do the Orthocentre lie in the given triangles.

Tags : Example Solved Problems | Practical Geometry , 9th Maths : UNIT 4 : Geometry

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9th Maths : UNIT 4 : Geometry : Construction of Orthocentre of a Triangle | Example Solved Problems | Practical Geometry

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