question_answer

Name the types of the following triangles:

(a) Triangle with lengths of sides 7 cm, 8 cm and 9 cm

(b) \[\Delta ABC\]with \[AB=8.7cm,\]AC = 7 cm and BC = 6 cm

(c) \[\Delta PQR\]such that PQ = QR = RP = 5 cm

(d) \[\Delta DEF\]with m\[\angle D\,\,=\,\,90{}^\circ \]

(e) \[\Delta XYZ\]with m\[\angle Y\,\,=\,\,90{}^\circ \]and XY = YZ

(f) \[\Delta LMN\]with mx\[\angle L\,\,=\,\,30{}^\circ ,\] \[\angle M\,\,=\,\,70{}^\circ ,\] m\[\angle N\,\,=\,\,80{}^\circ \]

Answer:

(a) Since all the sides are of different lengths.

\[\therefore \] It is scalene triangle.

(b) Since all the sides are unequal in \[\Delta ABC\].

\[\therefore \] \[\Delta ABC\] is scalene triangle.

(c) In \[\Delta PQR,\text{ }PQ=QR=RP\]

\[\therefore \] \[\Delta PQR\] is equilateral triangle.

(d) In \[\Delta DEF,\text{ }m\angle D=90{}^\circ \]

\[\therefore \] It is right angled triangle.

(e) In \[\Delta XYZ,\text{ }m\angle Y=90{}^\circ \] and  \[XY=YZ\]

\[\therefore \] It is isosceles right angled triangle.

(f) Since each angle of \[\Delta LMN\] is less than \[90{}^\circ \]

\[\therefore \] It is acute angled triangle.