D and E are respectively the points on the sides AB and AC of a \(\triangle\)ABC such that AB = 5.6 cm, AD = 1.4 cm, AC = 7.2 cm and AE = 1.8 cm, show that DE || BC

In the figure DE||AC and DC||AP. Prove that \(\frac { BE }{ CE } =\frac { BC }{ CP } \)

Construct a triangle \(\triangle\)PQR such that QR = 5 cm, \(\angle\)P = 30^o and the altitude from P to QR is of length 4.2 cm.

Draw a triangle ABC of base BC = 8 cm, \(\angle\)A = 60^o and the bisector of \(\angle\)A meets BC at D such that BD = 6 cm.

In Fig, ABC is a triangle with \(\angle\)B=90^o, BC=3cm and AB=4 cm. D is point on AC such that AD=1 cm and E is the midpoint of AB. Join D and E and extend DE to meet CB at F. Find BF.

In \(\triangle\)ABC , points D,E,F lies on BC, CA, AB respectively. Suppose AB, AC and BC have lengths 13, 14 and 15 respectively. If \(\frac { AF }{ FB } =\frac { 2 }{ 5 } \quad \frac { CE }{ EA } =\frac { 5 }{ 8 } \). Find BD an DC 

In a garden containing several trees, three particular trees P, Q, R are located in the following way, BP = 2 m, CQ = 3 m, RA = 10 m, PC = 6 m, QA = 5 m, RB = 2 m, where A, B, C are points such that P lies on BC, Q lies on AC and R lies on AB. Check whether the trees P, Q, R lie on a same straight line.

In \(AD\bot BC\) prove that AB² + CD² = BD² + AC². 

BL and CM are medians of a triangle ABC right angled at A.
Prove that 4(BL² + CM²) = 5BC².

Prove that in a right triangle, the square of 8. the hypotenure is equal to the sum of the squares of the others two sides.