Question

Step-1: Drawing a Quadrilateral o Draw a horizontal line AB of 5 cm length o Draw a ray ‘Ax’ from point A at an angle of 110° (using protractor) o Draw a second ray ‘By’ from point B at an angle of 70° (using protractor) o Cut the both these rays with arcs of 4 cm radius from points A & B respectively o Mark the left side intersection point as D and the right side intersection point as C o Join the points C and D with scale Now, we have a quadrilateral (i.e. polygon with 4 sides) • Step-2: Identifying the type of quadrilateral o Join A to C (what do we call the line segment AC?) o Measure angles ∠ACD and ∠CAB (How do they compare with each other?) o Measure angles ∠CAD and ∠ACB (How do they compare with each other?) ∴Line ABCD and line ADBC Quadrilateral in which each pair of opposite sides are parallel is known as PARALLELOGRAM • Step-3: Divide the parallelogram along the diagonal o Diagonal AC has divided the parallelogram ABCD into a set of 2 triangles i.e. ∆ABC and ∆ADC o Colour both triangles in two different shades o Measure their sides and angles. Tabulate them side by side in your note book o Calculate areas both triangles using Heron’s formula and write down in your note book Now, you might have observed that areas of ∆ABC and ∆ADC are same. If so, are these two ∆s congruent to each other? Let’s test it! • Step-4: Properties of a Parallelogram Concept congruency of triangles 1. Four criteria Viz. SSS, SAS, ASA & AAS are used to determine if two ∆s are congruent 2. If ∆s are found to be congruent, then their areas will be equal 3. Here, let us use the criteria SSS to check the congruency of these two ∆s, ∆ABC and ∆ADC. 4. Length measurements from the note book reveal that length of AB and CD are 5cm. 5. Similarly, length of AD and BC are 4 cm. 6. AC (the diagonal) is common between both ∆s ∴ Three sides of ∆ABC are same as that of ∆ADC It implies that both ∆ABC and ∆ADC are congruent to each other. It also confirms that the areas calculated using Heron’s formula earlier proves and confirms that the

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