Question

Draw 2 scalene triangles. In one triangle, draw all the medians and in the other triangle
draw all the altitudes. Do the altitudes and the medians meet at a point? If yes,
highlight the points in both the figures and name them.​

Answer 1

Given :   2 scalene triangles  

To Find  :   draw all the medians

draw all the altitudes.

Solution:

Step 1 : Draw a line segment  AB

Step 2 : Using suitable compass width other than AB and taking A as center draw an arc

Step 3 : Using suitable compass width different from previous step and AB , draw an arc taking B as center such that it intersects arc drawn in previous step at C

Stepp 4 : Join AC and BC

Draw  Median :   To  Draw median join Vertex of triangle with mid point of opposite side.

Find mid point of side using perpendicular bisector :

For example :

For BC  : Using suitable Equal compass width and taking B and C as center draw arcs both sides such that they intersects at X & Y

Join X & Y intersecting BC at  D

Then Join AD

Similarly Join BE and CF

Median meets at a point

To Find altitude :

Using suitable compass width and taking A  as center Draw arc intersecting BC at P & Q

Now using P and Q draw perpendicular bisector  passing through A and intersecting BC at D

Similarly BE and CF

Altitudes meets at a point.

Need to extend lines and altitude to complete the construction .  

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