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Class 9 Math Parallelograms and Triangles


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Class 9Class 10First YearSecond Year
2.Provethatthepointofconcurrencyofthemediansofatriangleandthetrianglewhichismadebyjoiningthemidpointsofitssidesisthesame.2. Prove that the point of concurrency of the medians of a triangle and the triangle which is made by joining the mid-points of its sides is the same.

ExampleThe bisectors of two angles on the same side of a parallelogram cut each other at right angles.
ExampleThe bisectors of two angles on the same side of a parallelogram cut each other at right angles.

ExampleThebisectorsoftwoanglesonthesamesideofaparallelogramcuteachotheratrightangles.ExampleThe bisectors of two angles on the same side of a parallelogram cut each other at right angles.

(iv) \mathrm{m} \angle 2 \cong \ldots \ldots
(iv)  \mathrm{m} \angle 2 \cong \ldots \ldots

(iv)m2(iv) \mathrm{m} \angle 2 \cong \ldots \ldots

1. Prove that a rilateral is a parallelogram if its(a) opposite angles are congruent.
1. Prove that a rilateral is a parallelogram if its(a) opposite angles are congruent.

1.Provethatarilateralisaparallelogramifits(a)oppositeanglesarecongruent.1. Prove that a rilateral is a parallelogram if its(a) opposite angles are congruent.

2. Take a line segment of length 5.5 \mathrm{~cm} and divide it into five congruent parts.[Hint: Draw an acute angle \angle \mathrm{BAX} . On \overline{\mathrm{AX}} take \overline{\mathrm{AP}} \cong \overline{\mathrm{PQ}} \cong \overline{\mathrm{QR}} \cong \overline{\mathrm{RS}} \cong \overline{\mathrm{ST}} .
2. Take a line segment of length  5.5 \mathrm{~cm}  and divide it into five congruent parts.[Hint: Draw an acute angle  \angle \mathrm{BAX} .  On  \overline{\mathrm{AX}}  take  \overline{\mathrm{AP}}   \cong \overline{\mathrm{PQ}} \cong \overline{\mathrm{QR}} \cong \overline{\mathrm{RS}} \cong \overline{\mathrm{ST}} .

2.Takealinesegmentoflength5.5 cmanddivideitintofivecongruentparts.[Hint:DrawanacuteangleBAX.OnAXtakeAPPQQRRSST.2. Take a line segment of length 5.5 \mathrm{~cm} and divide it into five congruent parts.[Hint: Draw an acute angle \angle \mathrm{BAX} . On \overline{\mathrm{AX}} take \overline{\mathrm{AP}} \cong \overline{\mathrm{PQ}} \cong \overline{\mathrm{QR}} \cong \overline{\mathrm{RS}} \cong \overline{\mathrm{ST}} .

3. Find the unknowns in the given figure.
3. Find the unknowns in the given figure.

3.Findtheunknownsinthegivenfigure.3. Find the unknowns in the given figure.

2. In parallelogram A B C D (i) \mathrm{m} \overline{\mathrm{AB}}
2. In parallelogram  A B C D (i)  \mathrm{m} \overline{\mathrm{AB}}

2.InparallelogramABCD(i)mAB2. In parallelogram A B C D (i) \mathrm{m} \overline{\mathrm{AB}}

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