Name: The Altitude of a Triangle
Uploaded: 2019-07-19
Duration: 2 min 45 s
Description: The orthocentre is made by intersecting the altitudes drawn from all the vertices to the triangle's opposite sides. But what is altitude? Watch this video to...

Question

Draw an isosceles triangle. Draw all of its medians and altitudes. Write your observation about their points of concurrence.

Accepted Answer

Isosceles triangle is a triangle with two equal sides. Angle opposite to equal sides are equal.

Step $1 :$ Draw base $B C$ of any length.

Step $2 :$ At $B$ , draw an acute angle of any measure.

Step $3 :$ At $C$ , draw acute angle of same measure as $∠ B$ .

Step $4 :$ Extend line from $B$ having drawn angle and extend line from $C$ having drawn angle. Mark the intersection point of both line as $A$ . Isosceles triangle $A B C$ is formed.

Step $5 :$ To draw medians, join each vertex with the mid points of opposite side. Name medians as $A P, B V, C U$ and mark the intersection of all medians as $G$ .

Step $6 :$ With $A$ as a centre and any convenient radius marks two points $M, N$ by drawing two arcs. From $M, N$ draw two arcs that intersect each other and mark intersection point as $T$ . Join $A T$ . In this way, altitude from $A$ is drawn, i.e., $A P$ .

Step $7 :$ Similarly, draw perpendiculars from each vertex on opposite sides, i.e., $A P, B Q, C R$ and mark intersection point of all altitudes as $O$ .

Observation - We observe that, in an isosceles triangle, the point of concurrence of medians (centroid) and altitudes (orthocentre) lie on the same straight line.

Draw an isosceles triangle. Draw all of its medians and altitudes. Write your observation about their points of concurrence.

Important Questions on Altitudes and Medians of a Triangle

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