Triangles are similar if both Triangles have same shape but it is not necessary that both triangles should have same size. Now we will discuss how to solve Similar Triangles:
Step 1: - First of all draw a line segment which is of length ‘x’ and then mark its end points as ‘a’ and ‘b’.
Step 2: - After that extend the given Line Segment beyond endpoints ‘a’ and ‘b’.
Step 3: - Draw a perpendicular to Point ‘ab’ at point ‘a’.
Step 4: - Now use compass to determine the point ‘o’ along perpendicular direction ‘ab’ at ‘a’ such that ao = 1.
Step 5: - Now mark another point ‘p’ on 'pr' such that ap = m.
Step 6: - Now connect the point ‘o’ and ‘b’ and we get a triangle.
Step 7: - Now copy the angle ‘abo’ at ‘p’ to form similar triangles. Mark the constructed Ray and ‘ab’ as ‘q’, point ‘p’ is between ‘a’ and ‘o’, and point ‘q’ is between ‘a’ and ‘b’, and if m = 1, then o = p and b = q.
This is the process of drawing similar triangles. We have some properties of similar triangles,
1. Corresponding angles of triangle are congruent (same measure),
2. Triangle's Corresponding Angles are in the same proportion.
When there are two triangles out of which one can be rotated, but both triangles have same shape, then also the triangles are similar. In case of similar triangles, one triangle can be a mirror image of another triangle. Similar triangles can also have shared parts i.e. two triangles can be similar, if they share same elements or property. This is how we can solve similar triangles.