1. Draw any triangle XYZ and name its sides, angles and vertices.
Sides = XY, YZ, ZX
Angles = ∠X, ∠Y, ∠Z (or) ∠YXZ, ∠XYZ, ∠XZY
Vertices = X, Y, Z
2. How many triangles are there in each of the following -
3 Triangles
5 Triangles
8 Triangles
8 Triangles
3. Identify the following triangles on the basis of their angles.
Right angled triangle
Obtuse angled triangle
Acute angled triangle
Acute angled triangle
4. Can we construct a triangle with angles of measure 70° , 40° , 60°? Why or Why not?
\[ \begin{align*} \text{Sum of angles} & = 70^\circ + 40^\circ + 60^\circ \\ & = 170^\circ \\ 180^\circ & \neq 170^\circ \end{align*} \]
No, because the sum of angles is not equal to 180°.
5. Can we construct a triangle using line segments of the following lengths?
\[ \begin{align*} & \text{Sum of two sides} && \text{Third Side} \\ & 7 + 6 = 13 & >\phantom{1} & 12 \\ & 6 + 12 = 18 & >\phantom{1} & 7 \\ & 7 + 12 = 19 & >\phantom{1} & 6 \\ \end{align*} \]
Yes, triangle is possible.
\[ \begin{align*} & \text{Sum of two sides} && \text{Third Side} \\ & 6 + 5 = 11 & =\phantom{1} & 11 \\ & 5 + 11 = 16 & >\phantom{1} & 6 \\ & 11 + 6 = 17 & >\phantom{1} & 5 \\ \end{align*} \]
No, triangle is not possible.
6. One of the angles of a right angled triangle is 40°. Find the other angles of the triangle.
In ΔABC, Sum of three angles of a triangle is 180°
\[ \begin{align*} \angle A + \angle B + \angle C & = 180^\circ \\ \angle A + 90^\circ + 40^\circ & = 180^\circ \\ \angle A + 130^\circ & = 180^\circ \\ \angle A & = 180^\circ - 130^\circ \\ \angle A & = 50^\circ \end{align*} \]
∠A = 50°, ∠B = 90°, ∠C = 40°
7. Two angles of a triangle measure 30° and 55° respectively. Find the measure of the third angle. Also state what type of a triangle is it.
In ΔXYZ, Sum of three angles of a triangle is 180°
\[ \begin{align*} \angle X + \angle Y + \angle Z & = 180^\circ \\ \angle X + 30^\circ + 55^\circ & = 180^\circ \\ \angle X + 85^\circ & = 180^\circ \\ \angle X & = 180^\circ - 85^\circ \\ \angle X & = 95^\circ \end{align*} \]
The third angle is 95° and it is an obtuse angled triangle.
8. Write 'True' or 'False' for the following statements.
True
False
True
True
False