Draw any triangle `A B C` . Bisect side `A B` at `D` . Through `D` , draw a line parallel to `B C` , meeting `A C` in `E` . Measure `A E` and `E C` .

Draw an /_B A C of measure 50^0 such that A B=5\ c m and A C=7\ c mdot Through C draw a line parallel to A B and through B draw a line parallel to AC, intersecting each other at Ddot Measure B D\ a n d\ C Ddot

Take any three non-collinear points A , B , C and draw \ A B C . Through each vertex of the triangle, draw a line parallel to the opposite side.

In Figure, A B C D E is a pentagon. A line through B parallel to A C meets D C produced at F . Show that: (i) a r( triangle A C B)=a r(triangle A C F) (ii) a r( quadrilateral A E D F)=a r(A B C D E)

In an isosceles triangle A B C with A B=A C , a circle passing through B\ a n d\ C intersects the sides A B\ a n d\ A C at D\ a n d\ E respectively. Prove that D E || B C .

D , E , F are the foot of the perpendicular from vertices A , B , C to sides B C ,\ C A ,\ A B respectively, and H is the orthocentre of acute angled triangle A B C ; where a , b , c are the sides of triangle A B C , then H is the incentre of triangle D E F A , B ,\ C are excentres of triangle D E F Perimeter of D E F is a cos A+b cos B+c\ cos C Circumradius of triangle D E F is R/2, where R is circumradius of A B C

A B C D is a quadrilateral. A line through D , parallel to A C , meets B C produced in P as shown in figure. Prove that a r (triangle A B P) =a r (Quad. A B C D) .

Fill in the blanks in the following so that each of the following statements is true. (i) Sides opposite to equal angles of a triangle are ....... (ii) Angle opposite to equal sides of a triangle are ....... (iii) In an equilateral triangle all angles are ....... (iv) In a A B C if /_A=/_C , then A B=\ ..... (v) If altitudes C E\ a n d\ B F of a triangle A B C are equal, then A B= ........ (vi) In an isosceles triangle A B C with A B=A C , if B D\ a n d\ C E are its altitudes, then B D is .......... C E . (vii) In right triangles A B C\ a n d\ D E F , if hypotenuse A B=E F and side A C=D E , then A B C\ ~= ....

If a line intersects sides AB and AC of a DeltaA B C at D and E respectively and is parallel to BC, prove that (A D)/(A B)=(A E)/(A C)

In A B C ,\ \ D E is parallel to base B C , with D on A B and E on A C . If (A D)/(D B)=2/3 , find (B C)/(D E) .

In triangle A B C , if A D is the bisector of /_A , prove that: (A r e a( A B D))/(A r e a( A C D))=(A B)/(A C)