In the adjoining figure, ΔCAB is a right triangle, right angled at A and AD ⊥ BC. Prove that ΔADB ~ ΔCDA. Further, if BC = 10 cm and CD = 2 cm, find the length of AD.

Converse of Basic Proportionality Theorem, AA Similarity Criterion for Triangles | PadhAiPro

Question

TextConverse of Basic Proportionality TheoremAA Similarity Criterion for TrianglesCBSE PYQ

Similar Questions

In the given figure, ABCD is a quadrilateral. Diagonal BD bisects ∠B and ∠D both. Prove that :

CASE_STUDIESConditions for Similarity of TrianglesAA Similarity Criterion for Triangles

If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then prove that the other two sides are divided in the same ratio.

Text

Basic Proportionality Theorem (Thales Theorem)

AA Similarity Criterion for Triangles

In the given figure PA, QB and RC are each perpendicular to AC. If AP = x, BQ = y and CR = z, then prove that 1/x + 1/z = 1/y

TextBasic Proportionality Theorem (Thales Theorem)AA Similarity Criterion for Triangles

P is a point on the side BC of ΔABC such that ∠APC = ∠BAC. Prove that AC² = BC · CP.

If a line drawn parallel to one side of triangle intersecting the other two sides in distinct points divides the two sides in the same ratio, then it is parallel to third side. State and prove the converse of the above statement.

TextConverse of Basic Proportionality TheoremAA Similarity Criterion for Triangles

Given △ABC ~ △PQR, ∠A = 30° and ∠Q = 90°. The value of (∠R + ∠B) is

MCQ (Single)Conditions for Similarity of TrianglesAA Similarity Criterion for Triangles