Question

In figure, ABC is an isosceles triangle in which AB=AC. Side BA is produced to D such that AD=AB. show that angle BCD is a right angle

Answer 1

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Answer 2

Figure:-

Given:-

• ABC is an isosceles triangle in which AB=AC. Side BA is produced to D such that AD=AB.

To prove:-

• <BCD is a right angle

Solutions:-

In ∆ACB,

AB = AC ⠀⠀⠀⠀⠀⠀⠀(Given)

<ACB = <ABC ⠀⠀(Angle opposite to equal side of triangle are also equal)

In ∆ACD,

AC = AD

<ADC = <ACD ⠀⠀(Angle opposite to equal side of a triangle are also equal)

In ∆BCD,

<ABC + <BCD + <ADC = 180° ⠀(Angle sum property of a triangle)

<ACB + <ACB + <ACD + <ACD = 180°

2 (<BCD) = 180°

<BCD = 180°/2

<BCD = 90°

Additional Information:-

• Straight line = Angle which measures 180°.
• Supplementary Angle = The two angle are supplementary, if there sum are 90°.
• Complementary Angle = The two angle are complementary, if these sum are 90°.