List of top Mathematics Questions on Similarity of Triangles asked in Bihar Board X

If one angle of a triangle is equal to one angle of the other triangle and the sides included between these angles are proportional then prove that the triangles are similar.
E is a point on the extended part of the side AD of a parallelogram ABCD and BE intersects CD at F; then prove that \(\triangle ABE \sim \triangle CFB\).
In a triangle PQR, two points S and T are on the sides PQ and PR respectively such that \(\frac{PS}{SQ} = \frac{PT}{TR}\) and \(\angle PST = \angle PRQ\), then prove that \(\triangle PQR\) is an isosceles triangle.
Sides AB and BC and median AD of a \(\triangle ABC\) are respectively proportional to sides PQ and QR and median PM of another \(\triangle PQR\). Then prove that \(\triangle ABC \sim \triangle PQR\).
\(\triangle ABC\) and \(\triangle DEF\) are similar and their areas are 9 cm\(^2\) and 64 cm\(^2\) respectively. If DE = 5.1 cm then find AB.
E is a point on side CB produced of an isosceles \(\triangle ABC\) with AB = AC. If AD \(\perp\) BC and EF \(\perp\) AC, prove that \(\triangle ABD \sim \triangle ECF\).
The corresponding sides of two similar triangles are in the ratio 4 : 9. What will be the ratio of the areas of the triangles?
\(\triangle ABC \sim \triangle DEF\) and BC = 3 cm, EF = 4 cm. If the area of \(\triangle ABC\) is 54 cm\(^2\), then the area of \(\triangle DEF\) is
\(\triangle ABC\) and \(\triangle DEF\) are such that \(\frac{AB}{DE} = \frac{BC}{EF} = \frac{CA}{DF}\) and \(\angle A = 40^\circ\), \(\angle B = 80^\circ\); then the measure of \(\angle F\) is
If the ratio of areas of two similar triangles is 100 : 144 then the ratio of their corresponding sides is