In the adjacent figure, \(\triangle\) ACB~\(\triangle\) APQ.If BC = 8 cm, PQ = 4 cm, BA = 6.5 cm and AP = 2.8 cm, find CA and AQ.

In \(\triangle\)ABC,D and E are points on the sides AB and AC respectively such that DE||BC \(\frac { AD }{ DB } =\frac { 3 }{ 4 } \) and AC = 15cm find AE.

In the rectangle WXYZ, XY+YZ = 17 cm, and XZ + YW = 26 cm .Calculate the length and breadth of the rectangle

D is the mid point of side BC and AE \(\bot \) BC. If BC = a, AC = b, AB = c, ED = x, AD = p and AE = h, prove that
\({ b }^{ 2 }={ p }^{ 2 }+ax+\frac { { a }^{ 2 } }{ 4 } \)

If figure OPRQ is a square and \(\angle\)MLN=90^o. Prove that

\(\triangle\)LOP~\(\triangle\)RPN

If figure OPRQ is a square and \(\angle\)MLN=90^o. Prove that

\(\triangle\)QMO ~\(\triangle\)RPN

If figure OPRQ is a square and \(\angle\)MLN = 90^o. Prove that

QR² = MQ x RN

In fig. if PQ || BC and PR || CD prove that

\(\frac { QB }{ AQ } =\frac { DR }{ AR } \)

D is the mid point of side BC and AE \(\bot \) BC. If BC = a, AC = b, AB = c, ED = x, AD = p and AE = h, prove that
\({ c }^{ 2 }={ p }^{ 2 }-ax+\frac { { a }^{ 2 } }{ 4 } \)

D is the mid point of side BC and AE \(\bot \) BC. If BC = a, AC = b, AB = c, ED = x, AD = p and AE = h, prove that
\({ b }^{ 2 }+{ c }^{ 2 }={ 2p }^{ 2 }+\frac { { a }^{ 2 } }{ 2 } \)