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Class 9 Math Sides and Angles of Triangle


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Class 9Class 10First YearSecond Year
Whichofthefollowingaretrueardwhicharefalse?(i)Theangleoppositetothelongersideofatriangleisgreater.(ii)Inarightangledtrianglegreaterangleisof60.(iii)Inanisoscelesrightangledtriangleanglesotherthanrightangleareeachof45.(iv)Atrianglehavingtwocongruentsidesiscalledequilateraltriangle.(v)Aperpendicularfromapointtoalineisshortestdistance.(vi)Perpendiculartolineformanangleof90.(vii)Apointoutsidethelineiscollinearwithit.(viii)Sumoftwosidesoftriangleisgreaterthanthethird.(ix)Thedistancebetweenalineandapointonitiszero.(x)Trianglecanbeformedoflengths2 cm3 cmand5 cm.Which of the following are true ard which are false?(i) The angle opposite to the longer side of a triangle is greater.(ii) In a right-angled triangle greater angle is of 60^{\circ} .(iii) In an isosceles right-angled triangle angles other than right angle are each of 45^{\circ} .(iv) A triangle having two congruent sides is called equilateral triangle.(v) A perpendicular from a point to a line is shortest distance.(vi) Perpendicular to line form an angle of 90^{\circ} .(vii) A point out side the line is collinear with it.(viii) Sum of two sides of triangle is greater than the third.(ix) The distance between a line and a point on it is zero.(x) Triangle can be formed of lengths 2 \mathrm{~cm} 3 \mathrm{~cm} and 5 \mathrm{~cm} .

6. If 3 \mathrm{~cm} and 4 \mathrm{~cm} are lengths of two sides of a right angle triangle then what should be the third length of the triangle.
6. If  3 \mathrm{~cm}  and  4 \mathrm{~cm}  are lengths of two sides of a right angle triangle then what should be the third length of the triangle.

6.If3 cmand4 cmarelengthsoftwosidesofarightangletrianglethenwhatshouldbethethirdlengthofthetriangle.6. If 3 \mathrm{~cm} and 4 \mathrm{~cm} are lengths of two sides of a right angle triangle then what should be the third length of the triangle.

4. Prove that in a right-angled triangle the hypotenuse is longer than each of the other two sides.
4. Prove that in a right-angled triangle the hypotenuse is longer than each of the other two sides.

4.Provethatinarightangledtrianglethehypotenuseislongerthaneachoftheothertwosides.4. Prove that in a right-angled triangle the hypotenuse is longer than each of the other two sides.

1. Two sides of a triangle measure 10 \mathrm{~cm} and 15 \mathrm{~cm} . Which of the following measure is possible for the third side?(b) 20 \mathrm{~cm}
1. Two sides of a triangle measure  10 \mathrm{~cm}  and  15 \mathrm{~cm} . Which of the following measure is possible for the third side?(b)  20 \mathrm{~cm}

1.Twosidesofatrianglemeasure10 cmand15 cm.Whichofthefollowingmeasureispossibleforthethirdside?(b)20 cm1. Two sides of a triangle measure 10 \mathrm{~cm} and 15 \mathrm{~cm} . Which of the following measure is possible for the third side?(b) 20 \mathrm{~cm}

1. In the figure P is any point and A B is a line. Which of the following is the shortest distance between the point \mathrm{P} and the line \mathrm{AB} ?(c) \mathrm{mPN}
1. In the figure  P  is any point and  A B  is a line. Which of the following is the shortest distance between the point  \mathrm{P}  and the line  \mathrm{AB}  ?(c)  \mathrm{mPN}

1.InthefigurePisanypointandABisaline.WhichofthefollowingistheshortestdistancebetweenthepointPandthelineAB?(c)mPN1. In the figure P is any point and A B is a line. Which of the following is the shortest distance between the point \mathrm{P} and the line \mathrm{AB} ?(c) \mathrm{mPN}

3. In the \triangle \mathrm{ABC} \mathrm{m} \angle \mathrm{B}=70^{\circ} and \mathrm{m} \angle \mathrm{C}=45^{\circ} . Which of the sides of the triangle is longest and which is the shortest?
3. In the  \triangle \mathrm{ABC} \mathrm{m} \angle \mathrm{B}=70^{\circ}  and  \mathrm{m} \angle \mathrm{C}=45^{\circ} . Which of the sides of the triangle is longest and which is the shortest?

3.IntheABCmB=70andmC=45.Whichofthesidesofthetriangleislongestandwhichistheshortest?3. In the \triangle \mathrm{ABC} \mathrm{m} \angle \mathrm{B}=70^{\circ} and \mathrm{m} \angle \mathrm{C}=45^{\circ} . Which of the sides of the triangle is longest and which is the shortest?

4. \cdots If 10 \mathrm{~cm} 6 \mathrm{~cm} and 8 \mathrm{~cm} are the lengths of a triangle then verify that sum of measures of two sides of a triangle is greater than the third side.
4.  \cdots  If  10 \mathrm{~cm} 6 \mathrm{~cm}  and  8 \mathrm{~cm}  are the lengths of a triangle then verify that sum of measures of two sides of a triangle is greater than the third side.

4.If10 cm6 cmand8 cmarethelengthsofatrianglethenverifythatsumofmeasuresoftwosidesofatriangleisgreaterthanthethirdside.4. \cdots If 10 \mathrm{~cm} 6 \mathrm{~cm} and 8 \mathrm{~cm} are the lengths of a triangle then verify that sum of measures of two sides of a triangle is greater than the third side.

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