Explain by connecting QS and PR, finding the different angles formed, and then using tringle congruence. Class 8
easyExplain by connecting QS and PR, finding the different angles formed, and then using tringle congruence. Class 8
Question 1.
Explain by connecting QS and PR, finding the different angles formed, and then using tringle congruence. Class 8
Solution:
QS and PR are perpendicular to each other, because QS and PR are parallel to two adjacent sides of the original square, which meet at right angle at each comer. Now all the eight right triangles are congruent to each other by SAS. Further, PQRS is made up of four triangles out of eight triangles. So, area of PQRS is half of the area of the original square.
Question 2.
Earlier, we saw a method to create a square with double the area of a given square paper. There is another method to do this in which two identical square papers are cut in the following way. Class 8
Can you arrange these pieces to create a square with double the area of either square?
Solution:
Yes. Arrange the four triangles as shown below :
