Q18 of 76 Page 11

In Fig. 10.140, X is a point in the interior of square ABCD.AXYZ is also a square. If DY = 3 cm and AZ = 2 cm, then BY =

∠Z = 90° (Angle of square)

Therefore, AZD is a right angle triangle,


By Pythagoras theorem,


AD2 = AZ2 + ZD2


AD2 = 22 + (2+3)2


AD2 = 4 + 25


AD = √29


In AXB, with​X as right angle,


By Pythagoras theorem,


AB2 = AX2 + XB2


XB2 = 29-4


XB = 5


BY = XB + XY


= 5 + 2


= 7cm

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In Fig. 10.138, if AE||DC and AB=AC, the value of ∠ABD is

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In Fig. 10.139, ABC is an isosceles triangle whose side AC is produced to E. Through C, CD is drawn parallel to BA. The value of x is

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In Fig. 10.141, ABC is a triangle in which ∠B =2∠C. D is a point on side such that AD bisects ∠BAC and AB=CD. BE is the bisector of ∠B. The measure of ∠BAC is


[Hint: Δ ABE ≅ Δ DCE]

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In Fig. 10.142, if AC is bisector of ∠BAD such that AB=3 cm and AC=5 cm, then CD=