• # 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 $m\angle N={{80}^{o}}.$

(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.