Triangle

If Delta_(1) is the area of the triangle formed by the centroid and two vertices of a triangle Delta_(2) is the area of the triangle formed by the mid- point of the sides of the same triangle, then Delta_(1):Delta_(2) =

AL, BM and CN are perpendicular from angular points of a triangle ABC on the opposite sides BC, CA and AB respectively. Delta is the area of triangle ABC, (r ) and R are the inradius and circumradius. If area of Delta LMN is Delta ', then the value of (Delta')/(Delta) is

In each of the following, state if the statement is true (T) or false (F). A triangle has three sides A triangle may have four vertices. Any three line-segment make up a triangle The interior of a triangle includes its vertices. The triangular region includes the vertices of the corresponding triangle. The vertices of a triangle are three collinear points. An equilateral triangle is scalene. Every right triangle is scalene. Each acute triangle is equilateral. No isosceles triangle is obtuse.

If the medians of a triangle A B C intersect at G , show that a r( triangle A G B)=a r( triangle A G C)=a r( triangle B G C)=1/3a r( triangle A B C) . GIVEN : triangle A B C such that its medians A D ,B E and C F intersect at G . TO PROVE : a r(triangle A G B)=a r( triangle B G C)=a r(triangle A G C)=1/3a r(triangle A B C)

If the medians of a triangle A B C intersect at G , show that a r( triangle A G B)=a r(triangle A G C)=a r(triangle B G C)=1/3a r( triangle A B C) . GIVEN : triangle A B C such that its medians A D ,B E and C F intersect at G TO PROVE : a r(triangle A G B)=a r(triangle B G C)=a r(triangle C G A)=1/3 ar (triangle A B C) .

A circumcircle is a circle which passes through all vertices of a triangle and an incircle is a circle which is inscribed in a triangle touching all sides of a triangle. Let ABC be a right-angled triangle whose radius of the circumcircle is 5 and its one side AB = 6. The radius of incircle of triangle ABC is r. Area of Delta ABC is

The triangle ABC, where A is (2, 6), B is (-3, 5) and C is (4, 7), is reflected in the y-axis to triangle A'B'C'. Triangle A'B'C' is then reflected in the origin to triangle A"B"C''. Write down a single transformation that maps triangle ABC onto triangle A"B"C".

Is it true to say that, if in two triangles, an angle of one triangle is equal to an angle of another triangle and two sides of one triangle are proportional to the two sides of the other triangle, then the triangles are similar? Give reason for your answer.

For which of the following change Delta H!=Delta U ?