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Q : Find the perimeter of each of the following shapes: (a) A triangle of sides 3 cm, 4 cm and 5 cm. (b) An equilateral triangle of side 9 cm. (c) An isosceles triangle with equal sides 8 cm each and third side 6 cm.
A:
A}
perimeter=3+4+5=12 cm
b}
perimeter=9×3=27 cm
c}
perimeter÷8+8+6=22 cm
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Gaurav Seth 4 years, 11 months ago
Given: ABC is an isosceles triangle in which AB = AC. AD bisects ∠PAC and CD || AB.
To Prove:
(i) ∠DAC = ∠BCA
(ii) ABCD is a parallelogram.
Proof:
(i) In ∆ABC,
∵ AB = AC
∴ ∠B = ∠C ...(1)
| Angles opposite to equal sides of a triangle are equal
Also, Ext. ∠PAC = ∠B + ∠C
| An exterior angle of a triangle is equal to the sum of two interior opposite angles
⇒ ∠PAC = ∠C + ∠C | From (1)
⇒ 2 ∠CAD = 2 ∠C | ∵ AD bisects ∠PAC
⇒ ∠CAD = ∠C
⇒ ∠DAC = ∠BCA
(ii) But these angles form a pair of equal alternate interior angles
∴ AD || BC
Also, CD || AB
∴ ABCD is a parallelogram
| A quadrilateral is a parallelogram if its both the pairs of opposite sides are parallel.
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Q: The diameter CD of a circle with Centre O is perpendicular to chord AB if AB is equal to 12 cm and CE=3cm, calculate the radius of the circle
E X P L A N A T I O N :
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