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 any triangle ABC. Bisect side AB at D. Through D, draw a line parallel to BC, meeting AC in E. Measure AE and EC .

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 the picture below, the side AC of the triangle ABC is extended by D, by adding the length of the side CB. Then the line through C parallel to DB is drawn to meet AB at E. Prove that CE bisects angle C

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

Fill in the blanks in the following so that each of the following statements is true Sides opposite to equal angles of a triangle are ....... Angle opposite to equal sides of a triangle are ....... In an opposite to equal sides of a triangle are ....... In a A B C if /_A=/_C , then A B= ..... If altitudes C E a n d B F of a triangle A B C are equal, then A B= ........ 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 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 ~= ....

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)