If in △ABC, AB AC and AD ⊥ BC, prove that AB 2 - AC 2 = BD 2 - CD 2 .

From figure, In right angle △ADB, By pythagoras theorem we get, AB 2 = AD 2 + BD 2 ........(i) In right angle △ADC, By pythagoras theorem we get, AC 2 = AD 2 + CD 2 ........(ii) Subtracting (ii) from (i), AB 2 - AC 2 = AD 2 + BD 2 - (AD 2 + CD 2 ) AB 2 - AC 2 = BD 2 - CD 2 . Hence, proved that AB 2 - AC 2 = BD 2 - CD 2 .

Mathematics

If in △ABC, AB > AC and AD ⊥ BC, prove that AB² - AC² = BD² - CD².

Pythagoras Theorem

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Answer

From figure,

If in △ABC, AB > AC and AD ⊥ BC, prove that AB^2 - AC^2 = BD^2 - CD^2. Pythagoras Theorem, ML Aggarwal Understanding Mathematics Solutions ICSE Class 9.

In right angle △ADB,

By pythagoras theorem we get,

AB² = AD² + BD² ……..(i)

In right angle △ADC,

By pythagoras theorem we get,

AC² = AD² + CD² ……..(ii)

Subtracting (ii) from (i),

AB² - AC² = AD² + BD² - (AD² + CD²)

AB² - AC² = BD² - CD².

Hence, proved that AB² - AC² = BD² - CD².

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Mathematics

If in △ABC, AB > AC and AD ⊥ BC, prove that AB² - AC² = BD² - CD².

Pythagoras Theorem

Answer

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Mathematics

If in △ABC, AB > AC and AD ⊥ BC, prove that AB2 - AC2 = BD2 - CD2.

Pythagoras Theorem

Answer

Related Questions

In the adjoining figure, △PQR is right angled at Q and points S and T trisect side QR. Prove that8PT2 = 3PR2 + 5PS2.

In a right angled triangle ABC, right angled at C, P and Q are the points on the sides CA and CB respectively which divide these sides in the ratio 2 : 1. Prove that(i) 9AQ2 = 9AC2 + 4BC2(ii) 9BP2 = 9BC2 + 4AC2(iii) 9(AQ2 + BP2) = 13AB2

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In the figure given below, ∠BAC = 90°, ADC = 90°, AD = 6 cm, CD = 8 cm and BC = 26 cm. Find(i) AC(ii) AB(iii) area of the shaded region.

If in △ABC, AB > AC and AD ⊥ BC, prove that AB² - AC² = BD² - CD².

In the adjoining figure, △PQR is right angled at Q and points S and T trisect side QR. Prove that
8PT² = 3PR² + 5PS².

In a right angled triangle ABC, right angled at C, P and Q are the points on the sides CA and CB respectively which divide these sides in the ratio 2 : 1. Prove that
(i) 9AQ² = 9AC² + 4BC²
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(i) AC
(ii) AB
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