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` .

Internal bisector of /_A of triangle ABC meets side BC at D. A line drawn through D perpendicular to AD intersects the side AC at E and the side AB at F. If a, b, c represent sides of DeltaABC, then

P is any point on base B C of A B C\ a n d\ D is the mid-point of B CdotD E is drawn parallel to P A to meet A C at Edot If a r\ ( A B C)=12 c m^2 , then find area of E Q 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 ~= ....

Triangles on the same base and between the same parallels are equal in area. GIVEN : Two triangles A B C and P B C on the same base B C and between the same parallel lines B C and A Pdot TO PROVE : a r( A B C)=a r( P B C) CONSTRUCTION : Through B , draw B D C A intersecting P A produced in D and through C , draw C Q B P , intersecting line A P in Q.

If triangle A B C is similar to triangle D E F such that B C=3C M ,E F=4c m and area of triangle A B C=54c m^2 . Determine the area of triangle D E Fdot

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

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

If A B C\ a n d\ D E F are two triangles such that A B ,\ B C are respectively equal and parallel to D E ,\ E F , then show that Quadrilateral A B E D is a parallelogram Quadrilateral B C F E is a parallelogram A C=D F (iv) A B C\ ~=\ D E F

A B C D is a cyclic quadrilateral. A Ba n dD C are produced to meet in Edot Prove that E B C-E D Adot

In Figure, triangle A B C is right-angled at Bdot Give that A B=9C M ,\ A C=15 C M ,\ a n d\ D ,\ E\ are the mid-points of the sides A B\ a n d\ A C respectively, calculate The length of B C (ii) The area of A D E