Question 6
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.
$\begin{matrix} T r i a n g l e & G i v e n m e a s u r e m e n t s 6. & Δ P Q R & P Q = 3.5 c m & Q R = 4 c m & P R = 3.5 c m \end{matrix}$

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Solution

To construct: $Δ$ PQR where PQ = 3.5 cm, QR = 4 cm and PR = 3.5 cm
Steps of construction:
(a) Draw a line segment QR=4 cm.
(b) Taking Q as centre and radius 3.5 cm, draw an arc.
(c) Similarly, taking R as centre and radius 3.5 cm, draw an another arc which intersects first arc at point P.
It is the required triangle PQR.

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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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