Congruent and similar triangles

You are going to draw a triangle onto card or paper You will need a ruler and compasses to construct it

Using a ruler and compasses only, this is how to construct a triangle of sides 8 cm, 7 cm & 4 cm On card, construct 2 triangles with sides 8 cm, 7cm & 4 cm Cut them out Put the point of compasses here & draw an arcs of radius 7 cm Put the point here & draw an arc of radius 4 cm 8 cm 7 cm4 cm Draw a line of 8 cm

Your two triangles are the same shape and size They are congruent

This is how to construct an equilateral triangle using a ruler and compasses On card, construct 2 equilateral triangles of different sizes. Cut them out. Put the point of compasses here & draw two arcs of equal radius Keep the radius the same, put point here & draw another arc

They are similar Your two triangles are the same SHAPE They are different SIZES

55º 75º Cut them out On card, draw 2 different triangles with base angles 75º and 55º Use a ruler and protractor Measure the third angles (They should both be 50º)

These two triangle have the same shape but They are similar triangles are different sizes They have the same angles

Which triangle is not similar to the others? Answer

These two triangles are both equilateral. Are they similar? Answer YES

Problems involving triangles can be solved by scale drawing

Scale drawings are similar to the real thing

N North Port Island The map shows the journey of a ship. MAP DRAWING Make a scale drawing & produce a similar diagram. The ship leaves the Port, sails 30 miles North, then 20 miles East. How far is the Island from the port ? ? I P

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