Question

construct a ∆DEF if DE=5cm, angle DEF=105° and angle EFD=40° .locate its orthocentre​

Answer 1

Given :  DE=5cm, angle DEF=105° and angle EFD=40°

To Find : construct   ∆DEF

Solution:

∠DEF=105°

∠EFD=40°

∠FDE=35°   (as sum of all angles of triangle = 180° )

Step 1  : Draw a line segment DE = 5 cm

Step 2 : Draw an angle of 105°  at E on DE using protractor

Step 3 : Draw an angle of 35°  at D on DE using protractor

Both angles intersects at F

Draw altitudes to get orthocenter

Example Altitude from E on DF

Using suitable compass width cut DF at X and Y

Using suitable compass width and taking X and Y as center draw intersecting arcs at Z

Draw a line passing though intersection point Z and  Vertex E  and meeting DF at M

EM is the required altitude

Similarly other altitudes can be drawn

Points at which altitudes intersects each other is called orthocenter.

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