question_answer 13)

Explain why \[\Delta ABC\cong \Delta FED\]

Answer:

                                \[\Delta ABC\cong \Delta FED\]                \[(={{90}^{o}})\] \[BC=ED\] \[\angle ACB=\angle FDE\] \[\left| \begin{align}   & \because \text{ The sum of the measures of three} \\  & \text{angles of atriangle is 18}{{\text{0}}^{\text{o}}} \\ \end{align} \right.\]                 \[\therefore \]  \[\Delta ABC\cong \Delta FED\] \[\left| \text{By SAS congruence criterion} \right.\]        Enrichment Activity. We saw that superposition is a useful method to test congruence of plane figures. We discussed conditions for congruence of line segments, angles and triangles. You can now try to extend this idea to other plane figures as well. 1.            Consider cut-outs of different sizes of squares. Use   the method of superposition to find out the condition for congruence of squares. How does the idea of' corresponding parts' under congruence apply? Are there corresponding sides? Are there corresponding diagonals? 2.            What happens if you take circles? What is the condition for congruence of two circles? Again, you can use the method of superposition. Investigate. 3.            Try to extend this idea to other plane figures like regular hexagons, etc. Take two congruent copies of a triangle. By paper folding, investigate if they have equal attitudes. Do they have equal medians? What can you say about their perimeters and areas. Sol.        1. The condition for congruence of squares is that their sides must be the same. 2.            The condition for congruence of two circles is that their radii must be the same, 3.            The condition for congruence of two plane figures like regular hexagons, etc. is that their sides must be the same. 4.            Two congruent triangles have equal altitudes, equal medians, equal altitudes, equal medians, equal perimeters and equal areas.