In the figure= B = 90°, AD² = AB? + BC2 + CD². Prove BCD= 90°.

1.	In the figure= B = 90°, AD² = AB? + BC2 + CD². Prove BCD= 90°.
Answer» Step-by-step EXPLANATION: Using Pythagoras theorem: AD² + BD² = AC² (= AB²) --- (1) CD² + BD² = BC² ------- (2) (2) - 2 * (1) => => CD² - BD² = BC² - 2 AC² + 2 AD² => = BC² - 2 (AD +CD)² + 2 AD² => = BC² - 2 CD² - 4 AD * CD => = BD² + CD² - 2 CD² -4 AD * CD => = BD² - CD² - 4 AD * CD Simplify to get BD² - CD² = 2 AD * CD

Answer»

Step-by-step EXPLANATION:

Using Pythagoras theorem:

AD² + BD² = AC² (= AB²) --- (1)

CD² + BD² = BC² ------- (2)

(2) - 2 * (1) =>

=> CD² - BD² = BC² - 2 AC² + 2 AD²

=> = BC² - 2 (AD +CD)² + 2 AD²

=> = BC² - 2 CD² - 4 AD * CD

=> = BD² + CD² - 2 CD² -4 AD * CD

=> = BD² - CD² - 4 AD * CD

Simplify to get

BD² - CD² = 2 AD * CD

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In the figure= B = 90°, AD² = AB? + BC2 + CD². Prove BCD= 90°.​

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In the figure= B = 90°, AD² = AB? + BC2 + CD². Prove BCD= 90°.