Read the following statements carefully. The question given below the statement are based on the clues given in the statements . Tick the correct option . Statement 1= A is not a hill station. Statement 2= B and E are not historical place. Statement 3= D is not an industrial center . Statement 4= A and D are not historical cities . Statement 5= S and B are not alike. Question 1= which city is a hill station and an industrial center but not a historical place (a) A (b) F (c) E (d) C
Answers
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Answer:
Q1. The angles of quadrilateral are in the ratio 3 : 5 : 9 : quadrilateral.
Sol: Let the angles of the quadrilateral be 3x, 5x, 9x and 13x.
∵ Sum of all the angles of quadrilateral = 360°
∴ 3x + 5x + 9x + 13x = 360°
⇒ 30x = 360°
∴ 3x = 3 × 12° = 36°
5x = 5 × 12°= 60°
9x = 9 × 12° = 108°
13x = 13 × 12° = 156°
⇒ The required angles of the quadrilateral are 36°, 60°, 108° and 156°.
Q2. If the diagonals of a parallelogram are equal, then show that it is a rectangle.
Sol: A parallelogram ABCD such that AC = BD In ΔABC and ΔDCB,
AC = DB
[Given]
AB = DC
[Opposite sides of a parallelogram]
BC = CB
[Common]
ΔABC = ΔDCB
[SSS criteria]
∴Their corresponding parts are equal.
⇒∠ABC = ∠DCB
...(1)
∵AB || DC and BC is a transversal.
[∵ ABCD is a parallelogram]
∴∠ABC + ∠DCB = 180°
...(2)
From (1) and (2), we have
∠ABC = ∠DCB = 90°
i.e. ABCD is parallelogram having an angle equal to 90°.
∴ABCD is a rectangle.
Q3. Show that if the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus.
hope it helpful