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##### Example \mathbf{A B C} is an isosceles triangle with base \overline{\mathbf{B C}} \cdot On \overrightarrow{\mathbf{B C}} a point \mathrm{D} is taken away from C. A line segment through D cuts \overline{\mathbf{A C}} at \mathbf{L} and \overline{\mathbf{A B}} at M . Prove that \mathrm{m} \overline{\mathbf{A L}}>\mathrm{m} \overline{\mathbf{A M}} .

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.

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. 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?

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.