Telangana SCERT Class 9 Math Solution Chapter 8 Quadrilaterals Exercise 8.1

Telangana SCERT Solution Class IX (9) Math Chapter 8 Quadrilaterals Exercise 8.1

(1) (i) Every parallelogram is a trapezium

(ii) All parallelograms are quadrilaterals

(iii) All trapeziums are parallelograms

(iv) A square is a rhombus

(v) Every rhombus is a square

(vi) All parallelograms are rectangles

(i) False, trapezium has only two side’s parallel.

(ii)  True

(iii) False, Parallel has opposite sided parallel

(iv) True

(v) False, A spare has to have all right angles bat a rhombus.

(v) False, a rectangle has to have all angles to be right angles.

(2) Complete the following table by writing (YES) if the property holds for the particular Quadrilateral and (NO) if property does not holds.

Properties Trapezium Parallelogram Rhombus Rectangle Square
a) only one pair of opposite sides are parallel Yes No No No No
b) Two pairs of opposite sided are parallel No Yes Yes Yes Yes
c) Opposite sides are equal No Yes Yes Yes Yes
d) Opposite angles are equal No Yes Yes Yes Yes
e) Consecutive angles are supplementary No Yes Yes Yes Yes
f) Diagonals bisects each other No Yes Yes Yes Yes
g) Diagonals are equal No No No Yes Yes
h) All sides are equal No No Yes No Yes
i) Each angled is right angles No No No Yes Yes
j) Diagonals are ____ to each other. No No Yes No Yes

(3) ABCD is trapezium in which AB || CD. If AD = BC, show that A = B and C = D

Solution: Given,

ABCD is a trapezium

AB ∥ CD, AC = BD

Now,

Draw two altitudes of trapezium ABCD

AP ⊥ CD ⊥ AQ [∵ AB ∥ CD]

BQ ⊥ CD ⊥ AB [∵ AB ∥ CD]

Now, In APD & BQC

(i) AD = ABC [given]

(ii) AP = BQ

Since, AP and BQ are two altitudes of the parallel side AB and CD

(iii) APD = BQC = 90o [AP ⊥CD & BQ ⊥ CD]

∴ △APD ≅ △BQC by RHS

∴ ∠DAP = ∠CBQ [∵ corresponding angles of congruent triangles are equal]

∠BAP = ∠ABQ = 90o [∵ AP ⊥ AB & BQ ⊥ AB]

∴ ∠A = BAP + DAP

= 90 + DAP

∠B = AŌQ + CBQ

= 90 + CBQ

∴ ∠A = ∠B [∵∠DAP = ∠CBQ] Hence shown

C = D [∵ corresponding angles of congruent triangles are equal] Hence shown.

(4) The four angles of a quadrilateral are in the ratio 1: 2:3:4. Find the measure of each angle of the quadrilateral.

Solution:  Given,

Ration of the angles of quadrilateral is 1 : 2 : 3 : 4

We know, sum of angles of a quadrilateral is 360o

Let, x be the factor that multiplies with each angle of the quadrillateral

x + 2x + 3x + 4x = 360o

Or, 10x = 360o

Or, x = 36o

∴ The measures of each angles of the quadrilateral are 1 x 36 = 36o, 2 x 36 = 72o, 3 x 36 = 108o,

4 x 36 = 144o

(5) ABCD is a rectangle AC is diagonal. Find the nature of ΔACD. Give reasons

Solution: Given,

ABCD is a rectangle

AC is the diagonal

∠B = 90o [all angles of a rectangle is 90o and opposite sides are parallel also adjacent sides are perpendicular to each other]

△ABC is a right angled triangle at ∠B = 90o with AC being the hypotenuse.

Updated: September 21, 2021 — 4:46 pm

7 Comments

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  1. Actually this 5th answer is wrong I think so

    1. Ss u are right

      1. Yep 3rd is also totally wrong

  2. Is there any mistake in representation of 3 answer

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