Fold the triangle so that the opposite sides meet and contain the vertex. The circumcentre of a right triangle lies at the midpoint of its hypotenuse.ġ.The circumcentre of an obtuse angled triangle lies in the exterior of the triangle.The circumcentre of an acute angled triangle lies in the interior of the triangle.Do you find anything special with the equilateral triangle in this case?Ĭheck if the following are true by paper-folding: The perpendicular bisectors of the sides of any triangle are concurrent.Īs done in the earlier activity on Centroid, you can repeat the experiment for various types of triangle, acute, obtuse, right, isosceles and equilateral. One can visualize the point of concurrence of the perpendicular bisectors, through simple paper folding. Can you identify the orthocentre in this case? In any obtuse angled triangle, the altitude connected to the obtuse vertex is inside the triangle, and the two altitudes connected to the acute vertices are outside the triangle. Can you identify the orthocentre in this case?ģ. In any right angled triangle, the altitude perpendicular to the hypotenuse is inside the triangle the other two altitudes are the legs of the triangle. In the interior of the triangle or in its exterior?Ģ. In any acute angled triangle, all three altitudes are inside the triangle. The point of concurrence is known as its Orthocentre, denoted by the letter H.ġ. The three altitudes of any triangle are concurrent. Do the altitudes of triangle pass through the same point? What is your conclusion? We see that, Also, with the help of your teacher, you find altitudes of right angled triangle and obtuse angled triangle. In the same way, you find altitudes of other two sides. The three medians of any triangle are concurrent. Now you can repeat this activity for an obtuse - angled triangle and a right triangle. Do the medians pass through the same point? In the same way, fold and draw the other two medians.Ħ. You can now draw the median AM, if you want to see it clearly. Fold the paper along the line that passes through the point A and meets the line BC such that point B falls on C. (Let us have an acute-angled triangle, to start with). Find all integer-sided right angled triangles with hypotenuse 85.ġ. (a, b, c) is a Pythagorean triplet if a = m 2 − n 2 , b = 2 mn and c = m 2 + n 2 (Think, why?)Ģ. Let m and n be any two positive integers (m > n): We can construct sets of Pythagorean triplets as follows. The students are asked to find which pair of triangles are similar or congruent based on the measures indicated in the triangles.ġ. The teacher cuts many triangles that are similar or congruent from a card board (or) chart sheet. (ii)Īre the triangles DBA and DBC congruent? Why?Īlso RHS rule also bind here to say their congruency. Match the following by their congruence propertyĪnswer: 1. Identify the pairs of figures which are similar and congruent and write the letter pairs. The exterior angle = sum of interior opposite angles.īut ∠ C = 40° Angles opposite to equal sides are _ and vice – versa. In a triangle, the sum of any two sides is _ than the third side. The exterior angle of a triangle is equal to the sum of the _ angles to it. The sum of the three angles of a triangle is _. Answer the following questions by recalling the properties of triangles:ġ.
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