Question

2.
In the figure, AB = AD prove that angle BCD is a right angle




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Answer 1

Answer:

this is the answer

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Answer 2

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Given

• AB = AC

• AD = AB

To Prove

• ∠BCD = 90°

Proof

In △ABC

AB = AC

∠ABC = ∠BCA [ Angles opposite to equal sides are also equal]

In △ADC

AC = AD

∠ACD = ∠ADC [ Angles opposite to equal sides are also equal]

➨∠D + ∠B + ∠C = 180° [ Angle Sum Property ]

➨∠ADC + ∠ACD + ∠ABC + ∠ACB = 180°

• ∠ACD = ∠ADC
• ∠ABC = ∠BCA

➨∠ACD + ∠ACD + ∠BCA + ∠BCA = 180°

➨2 ∠ACD + 2∠BCA = 180°

➨2 ( ∠ACD + ∠BCA ) = 180°

➨∠ACD + ∠BCA = 180°/ 2

➨∠ACD + ∠BCA = 90°

➨∠BCD = 90°

Hence, proved

Additionally

• Sum of any 2 sides of a triangle is always greater than the 3rd side.

• Angles opposite to equal sides of a triangle are equal.

• Sides opposite to equal sides of a triangle are equal.

• Angles opposite to larger side is longer.

• Side opposite to a larger angle is longer.