# Class 9 Math Practical Geometry _ Triangles 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?

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##### 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?

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 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 )

(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.

(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}

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}

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

(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.

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}

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}

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

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

(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

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}