Q1:In a ∆ ABC, AB = AC and D is a point on side AC, such that BC^2 = AC X CD .Prove that BD = BC.

Q2: If ∆ABC and ∆ AMP are two right triangles, right angled at B and M respectively such that angle MAP= angle BAC. Prove that ∆ ABC ~ ∆ AMP.

Q3: A vertical stick of length casts a shadow 4m long on the ground and at the same time a tower casts a shadow 28 m long .Find the height of the tower.

Q4:In ∆ABC, AD and BE are respectively perpendiculars to BC & AC. Show that ∆ADC ~ ∆BEC and CA x CE = CB x CD

Q5: E is a point on side AD produced of a parallelogram ABCD and BE intersects CD at F. Prove that ∆ABE ~ ∆ CFB.

Q6: Two sides and a median bisecting one of the sides of a triangle are respectively proportional to the two sides and the corresponding median of the other triangle. Prove that the triangles are similar.

Q7. E is a point on side AD produced of a parallelogram ABCD and BE intersects CD at F. prove that ∆ ABE ~ ∆CFB.

Q8.Prove that the area of the equilateral triangles describes on the side of a square is half the area of the equilateral triangle describes on its diagonals.

Q9. If∆ ABC ~ ∆ PQR and also ar (∆ABC)=4ar(∆PQR) If BC = 12cm, find QR.

Q10. ABC is a triangle right angled at A, AD is perpendicular to BC. IF BC = 13cm and AC = 5cm, find the ratio of the areas of ∆ABC and ∆ADC.

Q11. The area of two similar triangles is 121cm2 and 64cm2 respectively. If the median of the first triangle is 12.1cm, find the corresponding median of the other.

Q12. In an equilateral triangle with side `a`, Find the area of the triangle.

Q13. D and E are points on the sides AB and Ac respectively of ∆ABC such that DE is parallel to BC and AD: DB = 4: 5. CD and BE intersect each other at F. Find the ratio of the areas of ∆DEF & ∆BCF.

Q14. ∆ABC and ∆DEF are similar. The area of ∆ ABC is 9 cm2 and area of ∆DEF is 16 cm2. If BC = 2.1 cm, find the length of EF.

Q15.In a trapezium ABCD, O is the point of intersection of AC and BD, AB║CD and AB = 2 CD. If the area of ∆AOB = 84 cm2, find the area of ∆COD.

Q16.In two similar triangles ABC and PQR, if their corresponding altitudes AD and PS are in the ratio of 4: 9, find the ratio of the area of ∆ABC to that of ∆PQR.

Q17. D, E & F are the mid-points of the sides AB, CA and BC respectively of a ∆ABC. Using Area theorem of similar triangles, find the ratio of areas of triangles DEF and ABC.

Q18.ABC is a triangle and PQ is a straight line meeting AB in P and AC in Q. If AP = 1 cm, PB = 3cm, AQ = 1.5 cm, QC = 4.5 cm, Prove that the area of ∆ APQ is one-sixteenth of the area of ∆ABC.

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