Please answer 1st question

Please answer 1st question 4. PROBLEMS EXERCISE 84 square is inscribed in an isosceles right triangle so the square and the triangk have one angle common. Show that the vertex Ofthe "Pare opposite the vertex Of e common angle bisects the hym»tenuse. In a parallelogram ABCD, AB = 10 cm and AD • 6 cm. Ilie bisector of ZA meds DC in E. A E and BC produced mcet at F. Foul length of CE P. Q, R and S are respectively the mid+)ints Of the sides AB. BC. CD and DA Of a quadrilateral ABCD in which AC — BD. Prove that PQRS is a rhombus. p, Q. R and S are respectively the mid-points of the sides AB. BC. CD and DA a quadrilateral A BCD such that AC I BD. prove that PQRS is a . Q. R and S are respectively the midpints quadrilateral ABCD in which AC A diagonal ofa A Of 12. E and F: trapez.mr hint: 13. prove th 14. P and Show t square triln•g

∆ A B C i s a n i s o s c e l e s r i g h t t r i a n g l e a n d s q u a r e C P Q R i s i n s c r i b e d i n i t . g i v e n, C P Q R i s a s q u a r e . C P = P Q = Q R = R C ∆ A B C i s a n i s o s c e l e s t r i a n g l e ∴ A C = B C \Rightarrow A R + R C = C P + B P \Rightarrow A R = B P . . . . (i) [∵ R C = C P] i n ∆ A R Q a n d ∆ Q P B A R = B P ∠ A R Q = ∠ Q P B = 90 ° Q R = P Q ∴ ∆ A R Q ≅ ∆ Q P B \Rightarrow A Q = Q B ∴ Q b i s e c t s t h e h y p o t e n u s e A B