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Class 9 Math Line Bisectors and Angle Bisectors


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Mathcaret
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Real and Complex Numbers

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Logarithms

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Algebric Expressions and Algebric Formulas

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Factorization

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Algebric Manipulation

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Linear Equations and Inequalities

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Linear Graphs and their Applications

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Introduction to Coordinate Geometry

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Congruent Triangles

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Parallelograms and Triangles

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Line Bisectors and Angle Bisectors

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Sides and Angles of Triangle

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Ratio and Proportion

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Pythagoras's Theorem

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Theorems Related with Area

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Practical Geometry _ Triangles

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Physicscaret
Chemistrycaret
1.Whichofthefollowingaretrueandwhicharefalse?(i)Bisectionmeanstodivideintotwoequalparts.(ii)Rightbisectionoflinesegment.meanstodrawperpendicularwhichpassesthroughthemid−pointoflinesegment.(iii)Anypointontherightbisectorofalinesegmentisnotequidistantfromitsendpoints.(iv)Anypointequidistantfromtheendpointsofalinesegmentisontherightbisectorofit.(v)Therightbisectorsofthesidesofatrianglearenotconcurrent.(vi)Thebisectorsoftheanglesofatriangleareconcurrent.(vii)Anypointonthebisectorofanangleisnotequidistantfromitsarms.......(viii)Anypointinsideanangleequidistantfromitsarmsisonthebisectorofit.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.
2. Where will be the centre of a circle passing through three non-collinear points? And why?
2. Where will be the centre of a circle passing through three non-collinear points? And why?

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

5. In the given congruent triangles LMO and LNO
5. In the given congruent triangles LMO and LNO

5.InthegivencongruenttrianglesLMOandLNO5. In the given congruent triangles LMO and LNO

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

1.Provethatthebisectorsoftheanglesofbaseofanisosclestriangleintersecteachotheronitsaltitude.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} .
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} .

4.IfthegiventriangleABCisequilateraltriangleandAD‾isbisectorofangleAthenfindthevaluesofunknownsx∘y˙∘andz∘.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. 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.Thebisectorsof∠A∠Band∠CofarilateralABCPmeeteachotheratpointO.Provethatthebisectorof∠PwillalsopassthroughthepointO.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}}=
2. If \overleftarrow{\mathrm{CD}} is right bisector of line segment \overline{\mathrm{AB}} then(ii) \mathrm{m} \overline{\mathrm{AQ}}=

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

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