question_answer 32)

Name the types of following triangles. (a) Triangle with lengths of sides 7 cm, 8 cm and 9 cm. (b) \[\Delta ABC\] with AB = 8.7 cm, AC = 7 cm and BC = 6 cm. (c) \[\Delta PQR\] such that PQ = QR = PR = 5 cm. (d) \[\Delta DEF\]with \[m\angle D={{90}^{o}}\] (e) \[\Delta XYZ\]with \[m\angle Y={{90}^{o}}\] and XY = YZ. (f) \[\Delta LMN\] with \[m\angle L={{30}^{o}},m\angle M={{70}^{o}}\] and \[m\angle N={{80}^{o}}.\]

Answer:

(a) Given, first side = 7 cm; second side = 8 cm and third side = 9 cm where, \[7cm\ne 8cm\ne 9cm\] i.e. all the sides are of different length. So, it is a scalene triangle. (b) Given, AB = 8.7 cm, AC = 7 cm and BC = 6 cm where, \[AB\ne BC\ne CA\] i.e. all the sides are of different length. So, it is a scalene triangle. (c) Given, PQ = QR = PR = 5 cm i.e. all the sides are equal. So, it is an equilateral triangle. (d) Given, \[m\angle D={{90}^{o}}\] i.e. measure of \[\angle D\] is \[{{90}^{o}}\]. So, it is a right angled triangle. (e) Given, \[m\angle Y={{90}^{o}}\] i.e. measure of \[\angle Y={{90}^{o}}\]and XY = YZ Here, one angle is right angle and two sides are equal. So, it is an isosceles right angled triangle. (f) Given, \[m\angle L={{30}^{o}}\] i.e. measure of \[\angle L={{30}^{o}}\] (acute angle), \[m\angle M={{70}^{o}}\] i.e. measure of \[\angle M={{70}^{o}}\](acute angle) and \[m\angle N={{80}^{o}}\] i.e. measure of \[\angle N={{80}^{o}}\] (acute angle) Thus, all the angles are different and less than \[{{90}^{o}}\]. So, it is an acute angled triangle.