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

To do:

We have to name the types of triangles given.

Solution:

(a) A scalene triangle is a triangle in which all three sides are of different lengths, and all three angles are of different measures.

Therefore,

Triangle with lengths of sides $7 \mathrm{~cm}, 8 \mathrm{~cm}$ and $9 \mathrm{~cm}$ is a scalene triangle.

(b) A scalene triangle is a triangle in which all three sides are of different lengths, and all three angles are of different measures.

Therefore,

$\triangle \mathrm{ABC}$ with $\mathrm{AB}=8.7 \mathrm{~cm}, \mathrm{AC}=7 \mathrm{~cm}$ and $\mathrm{BC}=6 \mathrm{~cm}$ is a scalene triangle.

(c) An equilateral triangle is a triangle in which all three sides have the same length.

Therefore,

$\triangle \mathrm{PQR}$ such that $\mathrm{PQ}=\mathrm{QR}=\mathrm{PR}=5 \mathrm{~cm}$ is an equilateral triangle.

(d) A right triangle is a triangle in which one angle is a right angle.

Therefore,

$\triangle \mathrm{DEF}$ with $\mathrm{m} \angle \mathrm{D}=90^{\circ}$ is a right-angled triangle.

(e) An isosceles right triangle is defined as a right-angled triangle with an equal base and height.

Therefore,

$\triangle \mathrm{XYZ}$ with $\mathrm{m} \angle \mathrm{Y}=90^{\circ}$ and $\mathrm{XY}=\mathrm{YZ}$ is an Isosceles right triangle.

(f) An acute-angled triangle is a triangle in which all three interior angles are less than $90^o$.
Therefore,

$\Delta \mathrm{LMN}$ with $\mathrm{m} \angle \mathrm{L}=30^{\circ}, \mathrm{m} \angle \mathrm{M}=70^{\circ}$ and $\mathrm{m} \angle \mathrm{N}=80^{\circ}$ is a scalene triangle.

Updated on: 10-Oct-2022

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