# Class 9 Math Line Bisectors and Angle Bisectors 2. If \overleftarrow{\mathrm{CD}} is right bisector of line segment \overline{\mathrm{AB}} then

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##### 2. If \overleftarrow{\mathrm{CD}} is right bisector of line segment \overline{\mathrm{AB}} then

2. Where will be the centre of a circle passing through three non-collinear points? And why?

1. Prove that the bisectors of the angles of base of an isoscles triangle intersect each other on its altitude.

4. If the given triangle \mathrm{ABC} is equilateral triangle and \overline{\mathrm{AD}} is bisector of angle \mathrm{A} then find the values of unknowns x^{\circ} \dot{y}^{\circ} and z^{\circ} .

2. The bisectors of \angle \mathrm{A} \angle \mathrm{B} and \angle \mathrm{C} of a rilateral \mathrm{ABCP} meet each other at point \mathrm{O} . Prove that the bisector of \angle \mathrm{P} will also pass through the point \mathrm{O} .

2. If \overleftarrow{\mathrm{CD}} is right bisector of line segment \overline{\mathrm{AB}} then(ii) \mathrm{m} \overline{\mathrm{AQ}}=

3. Define the following(i) Bisector of a line segment

6. \overline{\mathrm{CD}} is right bisector of the line segment \mathrm{AB} .(i) If \mathrm{m} \overline{\mathrm{AB}}=6 \mathrm{~cm} then find the \mathrm{m} \overline{\mathrm{AL}} and \mathrm{mLB}

6. \overline{\mathrm{CD}} is right bisector of the line segment \mathrm{AB} .(ii) If \mathrm{m} \overline{\mathrm{BD}}=4 \mathrm{~cm} then find \mathrm{m} \overline{\mathrm{AD}} .

4. Prove that the altitudes of a triangle are concurrent.

1. Which of the following are true and which are false?(i) Bisection means to divide into two equal parts.(ii) Right bisection of line segment.means to draw perpendicular which passes through the mid-point of line segment.(iii) Any point on the right bisector of a line segment is not equidistant from its end points.(iv) Any point equidistant from the end points of a line segment is on the right bisector of it.(v) The right bisectors of the sides of a triangle are not concurrent.(vi) The bisectors of the angles of a triangle are concurrent.(vii) Any point on the bisector of an angle is not equidistant from its arms.......(viii) Any point inside an angle equidistant from its arms is on the bisector of it.

1. In a rilateral \mathrm{ABCD} \overline{\mathrm{AB}} \cong \overline{\mathrm{BC}} and the right bisectors of \overline{\mathrm{AD}} \overline{\mathrm{CD}} meet each other at point N . Prove that \overline{B N} is a bisector of \angle A B C .

3. Prove that the right bisectors of congruent sides of an isoscles triangle and its altitude are concurrent.

3. 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.

1. Prove that the centre of a circle is on the right bisectors of each of its chords.