10. In a quadrilateral ABCD, ZB = 90° and
AD^2 = AB^2 + BC^2 + CD^2. Prove that LACD = 90°
Answers
Answer:
✍️✍️Question:
In a quadrilateral ABCD, ZB = 90° and
AD²= AB² + BC² + CD² . Prove that LACD = 90°
✍️PYTHAGORAS THEOREM: In a right angle triangle the square of the hypotenuse is equal to the sum of the square of the other two sides.
✍️CONVERSE OF PYTHAGORAS THEOREM: In a triangle if square of one side is equal to the sum of the squares of the other two sides then the angle opposite to first side is a right angle.
✍️GIVEN:
A quadrilateral ABCD, ∠B =90°, AD² = AB² + BC² + CD²
✍️To Prove: ∠ACD = 90°
✍️PROOF:
AD² = AB² + BC² + CD²
AD² - CD² = AB² + BC² ……………(1)
In right ∆ABC, ∠B =90°,
AC² = AB² + BC²……………….(2)
[By Pythagoras theorem]
From eq 1 & 2
AC² = AD² - CD²
AC² + CD² = AD²
Therefore , ∠ACD = 90°
[By converse of Pythagoras theorem]
Hence, proved.✍️✍️✍️
Answer:
Question:
In a quadrilateral ABCD, ZB = 90° and
AD²= AB² + BC² + CD² . Prove that LACD = 90°
Solution:
PYTHAGORAS THEOREM: In a right angle triangle the square of the hypotenuse is equal to the sum of the square of the other two sides.
CONVERSE OF PYTHAGORAS THEOREM: In a triangle if square of one side is equal to the sum of the squares of the other two sides then the angle opposite to first side is a right angle.
GIVEN:
A quadrilateral ABCD, ∠B =90°, AD² = AB² + BC² + CD²
To Prove: ∠ACD = 90°
PROOF:
AD² = AB² + BC² + CD²
AD² - CD² = AB² + BC² …..(1)
In right ∆ABC, ∠B =90°,
AC² = AB² + BC².......(2)
[By Pythagoras theorem]
From eq 1 & 2
AC² = AD² - CD²
AC² + CD² = AD²
Therefore , ∠ACD = 90°
[By converse of Pythagoras theorem]
Hence proved,
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