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Class 9 Math Practical Geometry _ Triangles 1. Construct the following \Delta s \mathrm{ABC} . Draw the bisectors of their angles and verify their concurrency.(i) \mathrm{m} \overline{\mathrm{AB}}=4.5 \mathrm{~cm}


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1. Construct the following \Delta s \mathrm{ABC} . Draw the bisectors of their angles and verify their concurrency.(i) \mathrm{m} \overline{\mathrm{AB}}=4.5 \mathrm{~cm}

4. Construct the following \Delta \mathrm{s} \mathrm{XYZ} . Draw their three medians and show that they. are concurrent.(ii) \mathrm{m} \overline{\mathrm{XY}}=4.5 \mathrm{~cm} \mathrm{mYZ}=3.4 \mathrm{~cm} and \mathrm{mZX}=5.6 \mathrm{~cm}
4. Construct the following  \Delta \mathrm{s} \mathrm{XYZ} . Draw their three medians and show that they. are concurrent.(ii)  \mathrm{m} \overline{\mathrm{XY}}=4.5 \mathrm{~cm}   \mathrm{mYZ}=3.4 \mathrm{~cm}   and   \mathrm{mZX}=5.6 \mathrm{~cm}

4. Construct the following \Delta \mathrm{s} \mathrm{XYZ} . Draw their three medians and show that they. are concurrent.(ii) \mathrm{m} \overline{\mathrm{XY}}=4.5 \mathrm{~cm} \mathrm{mYZ}=3.4 \mathrm{~cm} and \mathrm{mZX}=5.6 \mathrm{~cm}

4. Construct a right-angled triangle equal in area to a given square.
4. Construct a right-angled triangle equal in area to a given square.

4. Construct a right-angled triangle equal in area to a given square.

4. Construct the following \Delta \mathrm{s} \mathrm{XYZ} . Draw their three medians and show that they. are concurrent.(iii) \mathrm{m} \overline{\mathrm{ZX}}=4.3 \mathrm{~cm}
4. Construct the following  \Delta \mathrm{s} \mathrm{XYZ} . Draw their three medians and show that they. are concurrent.(iii)  \mathrm{m} \overline{\mathrm{ZX}}=4.3 \mathrm{~cm}

4. Construct the following \Delta \mathrm{s} \mathrm{XYZ} . Draw their three medians and show that they. are concurrent.(iii) \mathrm{m} \overline{\mathrm{ZX}}=4.3 \mathrm{~cm}

5. (Ambiguous Case) Construct a \triangle \mathrm{ABC} in which(ii) \mathrm{m} \overline{\mathrm{BC}}=2.5 \mathrm{~cm} \mathrm{~m} \overline{\mathrm{AB}}=5.0 \mathrm{~cm} \mathrm{~m} \angle \mathrm{A}=30^{\circ} (one \Delta )
5. (Ambiguous Case) Construct a  \triangle \mathrm{ABC}  in which(ii)  \mathrm{m} \overline{\mathrm{BC}}=2.5 \mathrm{~cm}  \mathrm{~m} \overline{\mathrm{AB}}=5.0 \mathrm{~cm}  \mathrm{~m} \angle \mathrm{A}=30^{\circ}   (one  \Delta  )

5. (Ambiguous Case) Construct a \triangle \mathrm{ABC} in which(ii) \mathrm{m} \overline{\mathrm{BC}}=2.5 \mathrm{~cm} \mathrm{~m} \overline{\mathrm{AB}}=5.0 \mathrm{~cm} \mathrm{~m} \angle \mathrm{A}=30^{\circ} (one \Delta )

1. Construct a \Delta with sides 4 \mathrm{~cm} 5 \mathrm{~cm} and 6 \mathrm{~cm} and construct a rectangle having its area equal to that of the \Delta . Measure its diagonals. Are they equal?
1. Construct a  \Delta  with sides  4 \mathrm{~cm} 5 \mathrm{~cm}  and  6 \mathrm{~cm}  and construct a rectangle having its area equal to that of the  \Delta . Measure its diagonals. Are they equal?

1. Construct a \Delta with sides 4 \mathrm{~cm} 5 \mathrm{~cm} and 6 \mathrm{~cm} and construct a rectangle having its area equal to that of the \Delta . Measure its diagonals. Are they equal?

(viii) The medians of a triangle cut each other in the ratio \ldots \ldots (a) 4: 1 (b) 3: 1 (c) 2: 1 (d) 1: 1
(viii) The medians of a triangle cut each other in the ratio  \ldots \ldots (a)  4: 1 (b)  3: 1 (c)  2: 1 (d)  1: 1

(viii) The medians of a triangle cut each other in the ratio \ldots \ldots (a) 4: 1 (b) 3: 1 (c) 2: 1 (d) 1: 1

Example(ii) Draw its angle bisectors and verify that they are concurrent.
Example(ii) Draw its angle bisectors and verify that they are concurrent.

Example(ii) Draw its angle bisectors and verify that they are concurrent.

(iii) The right bisectors of the three sides of a triangle are ......(a) congruent(b) collinear(c) concurrent(d) parallel
(iii) The right bisectors of the three sides of a triangle are ......(a) congruent(b) collinear(c) concurrent(d) parallel

(iii) The right bisectors of the three sides of a triangle are ......(a) congruent(b) collinear(c) concurrent(d) parallel

1. Construct a \triangle \mathrm{ABC} in which(vii) \mathrm{m} \overline{\mathrm{AB}}=3.6 \mathrm{~cm} \mathrm{m} \angle \mathrm{A}=75^{\circ} \mathrm{m} \angle \mathrm{B}=45^{\circ}
1. Construct a  \triangle \mathrm{ABC}  in which(vii)  \mathrm{m} \overline{\mathrm{AB}}=3.6 \mathrm{~cm}  \mathrm{m} \angle \mathrm{A}=75^{\circ}  \mathrm{m} \angle \mathrm{B}=45^{\circ}

1. Construct a \triangle \mathrm{ABC} in which(vii) \mathrm{m} \overline{\mathrm{AB}}=3.6 \mathrm{~cm} \mathrm{m} \angle \mathrm{A}=75^{\circ} \mathrm{m} \angle \mathrm{B}=45^{\circ}

4. Construct a right-angled isosceles triangle whose hypotenuse is(iii) 6.2 \mathrm{~cm}
4. Construct a right-angled isosceles triangle whose hypotenuse is(iii)  6.2 \mathrm{~cm}

4. Construct a right-angled isosceles triangle whose hypotenuse is(iii) 6.2 \mathrm{~cm}

4. Construct the following \Delta \mathrm{s} \mathrm{XYZ} . Draw their three medians and show that they. are concurrent.(i) \mathrm{m} \overline{\mathrm{YZ}}=4.1 \mathrm{~cm}
4. Construct the following  \Delta \mathrm{s} \mathrm{XYZ} . Draw their three medians and show that they. are concurrent.(i)  \mathrm{m} \overline{\mathrm{YZ}}=4.1 \mathrm{~cm}

4. Construct the following \Delta \mathrm{s} \mathrm{XYZ} . Draw their three medians and show that they. are concurrent.(i) \mathrm{m} \overline{\mathrm{YZ}}=4.1 \mathrm{~cm}

Example(ii) Draw perpendicular bisectors of its sides and verify that they are concurrent.
Example(ii) Draw perpendicular bisectors of its sides and verify that they are concurrent.

Example(ii) Draw perpendicular bisectors of its sides and verify that they are concurrent.

(ii) A rilateral having each angle equal ot 90^{\circ} is called ......(a) parallelogram(b) rectangle(c) trapezium(d) rhombus
(ii) A rilateral having each angle equal ot  90^{\circ}  is called ......(a) parallelogram(b) rectangle(c) trapezium(d) rhombus

(ii) A rilateral having each angle equal ot 90^{\circ} is called ......(a) parallelogram(b) rectangle(c) trapezium(d) rhombus

3. Define the following(iv) Centroid
3. Define the following(iv) Centroid

3. Define the following(iv) Centroid

(ix) One angle on the base of an isosceles triangle is 30^{\circ} . What is the measure of its vertical angle.(a) 30^{\circ} (b) 60^{\circ} (c) 90^{\circ} (d) 120^{\circ}
(ix) One angle on the base of an isosceles triangle is  30^{\circ} . What is the measure of its vertical angle.(a)  30^{\circ} (b)  60^{\circ} (c)  90^{\circ} (d)  120^{\circ}

(ix) One angle on the base of an isosceles triangle is 30^{\circ} . What is the measure of its vertical angle.(a) 30^{\circ} (b) 60^{\circ} (c) 90^{\circ} (d) 120^{\circ}

2. Transform an isosceles \Delta into a rectangle.
2. Transform an isosceles  \Delta  into a rectangle.

2. Transform an isosceles \Delta into a rectangle.

1. Construct a \triangle \mathrm{ABC} in which(v) \mathrm{mBC}=4.2 \mathrm{~cm}
1. Construct a  \triangle \mathrm{ABC}  in which(v)  \mathrm{mBC}=4.2 \mathrm{~cm}

1. Construct a \triangle \mathrm{ABC} in which(v) \mathrm{mBC}=4.2 \mathrm{~cm}

1. Construct a \triangle \mathrm{ABC} in which(iii) \mathrm{m} \overline{\mathrm{AB}}=4.8 \mathrm{~cm}
1. Construct a  \triangle \mathrm{ABC}  in which(iii)  \mathrm{m} \overline{\mathrm{AB}}=4.8 \mathrm{~cm}

1. Construct a \triangle \mathrm{ABC} in which(iii) \mathrm{m} \overline{\mathrm{AB}}=4.8 \mathrm{~cm}

5. (Ambiguous Case) Construct a \triangle \mathrm{ABC} in which(i) \mathrm{m} \overline{\mathrm{AC}}=4.2 \mathrm{~cm} \mathrm{~m} \overline{\mathrm{AB}}=5.2 \mathrm{~cm} \mathrm{~m} \angle \mathrm{B}=45^{\circ} ( two \Delta \mathrm{s})
5. (Ambiguous Case) Construct a  \triangle \mathrm{ABC}  in which(i)  \mathrm{m} \overline{\mathrm{AC}}=4.2 \mathrm{~cm}  \mathrm{~m} \overline{\mathrm{AB}}=5.2 \mathrm{~cm}  \mathrm{~m} \angle \mathrm{B}=45^{\circ} (  two  \Delta \mathrm{s})
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5. (Ambiguous Case) Construct a \triangle \mathrm{ABC} in which(i) \mathrm{m} \overline{\mathrm{AC}}=4.2 \mathrm{~cm} \mathrm{~m} \overline{\mathrm{AB}}=5.2 \mathrm{~cm} \mathrm{~m} \angle \mathrm{B}=45^{\circ} ( two \Delta \mathrm{s})

1. Construct the following \Delta s \mathrm{ABC} . Draw the bisectors of their angles and verify their concurrency.(i) \mathrm{m} \overline{\mathrm{AB}}=4.5 \mathrm{~cm}
1. Construct the following  \Delta  s  \mathrm{ABC} . Draw the bisectors of their angles and verify their concurrency.(i)  \mathrm{m} \overline{\mathrm{AB}}=4.5 \mathrm{~cm}
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1. Construct the following \Delta s \mathrm{ABC} . Draw the bisectors of their angles and verify their concurrency.(i) \mathrm{m} \overline{\mathrm{AB}}=4.5 \mathrm{~cm}

2. Construct the following \Delta s \mathrm{PQR} . Draw their altitudes and show that they are concurrent.(i) \mathrm{m} \overline{\mathrm{PQ}}=6 \mathrm{~cm} \mathrm{m} \overline{\mathrm{QR}}=4.5 \mathrm{~cm} and \mathrm{mPR}=5.5 \mathrm{~cm}
2. Construct the following  \Delta  s  \mathrm{PQR} . Draw their altitudes and show that they are concurrent.(i)  \mathrm{m} \overline{\mathrm{PQ}}=6 \mathrm{~cm}  \mathrm{m} \overline{\mathrm{QR}}=4.5 \mathrm{~cm} and  \mathrm{mPR}=5.5 \mathrm{~cm}
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2. Construct the following \Delta s \mathrm{PQR} . Draw their altitudes and show that they are concurrent.(i) \mathrm{m} \overline{\mathrm{PQ}}=6 \mathrm{~cm} \mathrm{m} \overline{\mathrm{QR}}=4.5 \mathrm{~cm} and \mathrm{mPR}=5.5 \mathrm{~cm}

(x) If the three altitudes of a triangle are congruent then the triangle is(a) equilateral(b) right angled(c) isosceles(d) acute angled
(x) If the three altitudes of a triangle are congruent then the triangle is(a) equilateral(b) right angled(c) isosceles(d) acute angled
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(x) If the three altitudes of a triangle are congruent then the triangle is(a) equilateral(b) right angled(c) isosceles(d) acute angled

Example(i) Construct a \triangle \mathrm{ABC} having given \mathrm{m} \overline{\mathrm{AB}}=4.6 \mathrm{~cm} \mathrm{~m} \overline{\mathrm{BC}}=5 \mathrm{~cm} and \mathrm{m} \overline{\mathrm{CA}}=5.1 \mathrm{~cm} .
Example(i) Construct a  \triangle \mathrm{ABC}  having given  \mathrm{m} \overline{\mathrm{AB}}=4.6 \mathrm{~cm} \mathrm{~m} \overline{\mathrm{BC}}=5 \mathrm{~cm}  and  \mathrm{m} \overline{\mathrm{CA}}=5.1 \mathrm{~cm} .
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Example(i) Construct a \triangle \mathrm{ABC} having given \mathrm{m} \overline{\mathrm{AB}}=4.6 \mathrm{~cm} \mathrm{~m} \overline{\mathrm{BC}}=5 \mathrm{~cm} and \mathrm{m} \overline{\mathrm{CA}}=5.1 \mathrm{~cm} .

(xi) It two medians of a triangle are congruent then the triangle will be ......(a) isosceles(b) equilateral(c) right angled(d) acute angled
(xi) It two medians of a triangle are congruent then the triangle will be ......(a) isosceles(b) equilateral(c) right angled(d) acute angled
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(xi) It two medians of a triangle are congruent then the triangle will be ......(a) isosceles(b) equilateral(c) right angled(d) acute angled

(vi) \ldots \ldots congruent triangles can be made by joining the mid-points of the sides of a triangle.(a) three(b) four(c) five(d) two
(vi)  \ldots \ldots  congruent triangles can be made by joining the mid-points of the sides of a triangle.(a) three(b) four(c) five(d) two
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(vi) \ldots \ldots congruent triangles can be made by joining the mid-points of the sides of a triangle.(a) three(b) four(c) five(d) two

(v) A point equidistant from the end points of a line-segment is on its(a) bisector(b) right-bisector(c) perpendicular(d) median
(v) A point equidistant from the end points of a line-segment is on its(a) bisector(b) right-bisector(c) perpendicular(d) median
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(v) A point equidistant from the end points of a line-segment is on its(a) bisector(b) right-bisector(c) perpendicular(d) median

4. Construct a right-angled isosceles triangle whose hypotenuse is(ii) 4.8 \mathrm{~cm}
4. Construct a right-angled isosceles triangle whose hypotenuse is(ii)  4.8 \mathrm{~cm}
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4. Construct a right-angled isosceles triangle whose hypotenuse is(ii) 4.8 \mathrm{~cm}

3. Construct the following triangles ABC. Draw the perpendicular bisectors of their sides and verify their concurrency. Do they meet inside the triangle?(ii) \mathrm{m} \overline{\mathrm{BC}}=2.9 \mathrm{~cm} \mathrm{~m} \angle \mathrm{A}=30^{\circ} \mathrm{m} \angle \mathrm{B}=60^{\circ}
3. Construct the following triangles ABC. Draw the perpendicular bisectors of their sides and verify their concurrency. Do they meet inside the triangle?(ii)  \mathrm{m} \overline{\mathrm{BC}}=2.9 \mathrm{~cm}  \mathrm{~m} \angle \mathrm{A}=30^{\circ}  \mathrm{m} \angle \mathrm{B}=60^{\circ}
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3. Construct the following triangles ABC. Draw the perpendicular bisectors of their sides and verify their concurrency. Do they meet inside the triangle?(ii) \mathrm{m} \overline{\mathrm{BC}}=2.9 \mathrm{~cm} \mathrm{~m} \angle \mathrm{A}=30^{\circ} \mathrm{m} \angle \mathrm{B}=60^{\circ}

3. Define the following(v) Point of concurrency
3. Define the following(v) Point of concurrency
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3. Define the following(v) Point of concurrency

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