Q : 1 ABCD is a quadrilateral in which P, Q, R and S are mid-points of the sides AB, BC, CD and DA (see Fig ). AC is a diagonal. Show that :
(iii) PQRS is a parallelogram.
4. Complete the hexagonal and star shaped Rangolies [see Fig. (i) and (ii)] by filling them with as many equilateral triangles of side cm as you can. Count the number of triangles in each case. Which has more triangles?
3. In a huge park, people are concentrated at three points (see Fig.):
A : where there are different slides and swings for children,
B : near which a man-made lake is situated,
C : which is near to a large parking and exit.
Where should an icecream parlour be set up so that maximum number of persons can approach it?
(Hint : The parlour should be equidistant from A, B and C)
2. In a triangle locate a point in its interior which is equidistant from all the sides of the triangle.
1. ABC is a triangle. Locate a point in the interior of which is equidistant from all the vertices of .
6. Show that of all line segments drawn from a given point not on it, the perpendicular line segment is the shortest.
4. AB and CD are respectively the smallest and longest sides of a quadrilateral ABCD (see Fig.). Show that and .
4. BE and CF are two equal altitudes of a triangle ABC. Using RHS congruence rule, prove that the triangle ABC is isosceles.
3. Two sides AB and BC and median AM of one triangle ABC are respectively equal to sides PQ and QR and median PN of (see Fig). Show that:
1.(iv) and are two isosceles triangles on the same base BC and vertices A and D are on the same side of BC (see Fig.). If AD is extended to intersect BC at P, show that
(iv) AP is the perpendicular bisector of BC.
1.(iii) and are two isosceles triangles on the same base BC and vertices A and D are on the same side of BC (see Fig.). If AD is extended to intersect BC at P, show that
(iii) AP bisects as well as .