Math 9th Chapter # 12 Exercise # 12.3 Question # 1

Math 9th class Chapter # 12, Exercise # 12.3 Question # 1 Prove that the bisectors of the angles of base of an isosceles triangle intersect each other on its altitude. In a quadrilateral ABCD, AB=BC and the right bisectors of AD, CD meet each other at point N, Prove that BN is a bisector of angle ABC. Three villages P, Q and R are not on the same line. The people of these villages want to make a Children Park at such a place which is equidistant from these three villages. After fixing the place of Children Park. prove that the Park is equidistant from the three villages. Math 9th class Chapter # 10,Exercise # 10.1 Question # 2 From a point on the bisector of an angle, perpendiculars are drawn to the arms of the angle. Prove that these perpendiculars are equal in measure. If in the correspondence of two right angled triangles, the hypotenuse and one side of one respectively congruent to the hypotenuse and corresponding side of other, the triangles are congruent. Math 9th class Chapter # 10, Theorem # 10.1.3 In any two corresponding triangles if three sides of one triangle are congruent to the other, than the triangles are congruent. In any correspondence of two triangles, if one side and any two angles of one triangle are congruent to the corresponding side and angles of the other, then triangles are congruent. Exercise # 9.3, Question # 6: - The vertices of a triangle are P (4 , 6), Q(-2 , -4) and R(-8 , 2). Show that the length of the line segment joining the mid-points of the line segments PR, QR is 1/2PQ. Question # 5 :- Show that the diagonals of the parallelogram having vertices A(1,2), B(4,2), C(-1,-3) and D(-4,-3) bisect each other. Question# 4 : if O(0 ,0) and B (3 , 0) and B(3 , 5) are three points in the plane, find M1 and M2 as mid-points of the line segments AB and OB respectively. Find IM1M2) Question # 3 Question# 3 Prove that midpoint of the hypotenuse of a right triangle is equidistance from three vertices P( -2, 5), Q(1, 3 and R(-1, 0). Question # 9 Show that the points M(-1 , 4), N(-5 , 3), P(1 , -3 and Q (5 , -2) are the vertices of a Parallelogram. Question # 10 Find the length of the diameter of the circle having center at C(-3 , 6) and passing P( 1, 3). Math 9th Class Chapter # 9.2 Question # 3 Show whether the points with coordinates (1 , 3 ) , (4, 2) and (-2, 6) are vertices of the right triangle. Question # 4 Use the distance formula to prove whether or not the points (1, 1) (-2, 8) and (4, 10) lie on the starlight line. Show whether the points with vertices (5, -2), (5 , 4) and (-4, 1) are the vertices of equilateral triangle or isosceles triangle. Question # 2 Show whether are not the points with vertices (-1, 1), (2, -2) and (-4, 1) form a square.