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How to construct similar triangles with ruler or compass ?

Use the same angles from the first triangle, find the proportional change between the first and new base segments, correspond this proportion to the other sides. ie. a base segment of 3 inches to 5 inches would be a proportional change of 5/3. so a side that is originally 6 inches would then be 10 inches. 6 * (5/3) = 10

Use the same angles from the first triangle, find the proportional change between the first and new base segments, correspond this proportion to the other sides. ie. a base segment of 3 inches to 5 inches would be a proportional change of 5/3. so a side that is originally 6 inches would then be 10 inches. 6 * (5/3) = 10

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**There are some steps through which we can understand how to construct similar Triangles. Triangles are similar if they have same shape but in the same triangle it is not necessary that the triangle have same size. Steps for construction of Similar Triangles:**

Step1: - First of all we draw a line segment which is of length ‘x’ and then we mark its end points as m and ‘n’.

Step2: - After that we extend the given Line Segment beyond the endpoints ‘m’ and ‘n’.

Step3: - Draw a perpendicular to Point ‘mn’ at point ‘m’.

Step4: - Now use compass to determine the point ‘o’ along to the perpendicular direction ‘mn’ at ‘m’ such as mo = 1.

Step5: - Now we determine another point ‘p’ on pr such as mp = b.

Step6: - Now we connect the point ‘o’ and ‘n’ and we get a triangle.

Step7: - Now copy the angle ‘mno’ at ‘p’ to form similar triangles. Mark the constructed Ray and ‘mn’ as ‘q’, then we find that the point ‘p’ is between ‘m’ and ‘o’, and point ‘q’ is between ‘m’ and ‘n’, and if b = 1, then o = p and n = q.

**This way we get the similar triangles. We have some properties of similar triangles**

1. Corresponding angles of the triangle are congruent (same measure),

2. In the triangles Corresponding Angles are in the same proportion.

When there are two triangles out of which one can be rotated, but both the triangles have same shape, then also the triangles are similar. In case of similar triangle, one triangle can be a mirror image of the other triangle. Similar triangles can also have shared parts i.e. two triangles can be similar, if they share some elements or property. When we go through above steps of triangle we get similar triangles.