Question 8
Below are given the measures of certain sides and angles of triangles. Identify those which cannot be constructed and, say why you cannot construct them. Construct rest of the triangle.
$\begin{matrix} T r i a n g l e & G i v e n m e a s u r e m e n t s 8. & Δ D E F & D E = 4.5 c m & E F = 5.5 c m & D F = 4 c m \end{matrix}$

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Solution

To construct: A triangle DEF whose sides are DE = 4.5 cm, EF = 5.5 cm and DF = 4 cm.
Steps of construction:

(a) Draw a line segment EF = 5.5 cm.
(b) Taking E as centre and radius 4.5 cm, draw an arc.
(c) Taking F as centre and radius 4 cm, draw an another arc which intersects the first arc at point D.
It is the required triangle DEF.

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\begin{matrix} T r i a n g l e & G i v e n m e a s u r e m e n t s 5. & Δ A B C & B C = 2 c m & A B = 4 c m & A C = 2 c m \end{matrix}

\begin{matrix} T r i a n g l e & G i v e n m e a s u r e m e n t s 7. & Δ X Y Z & X Y = 3 c m & Y Z = 4 c m & X Z = 5 c m \end{matrix}

Look at the given measure of sides and angles of the triangles, which of the following triangle cannot be constructed?

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