ABC is an isosceles triangle with ab = AC and D is a point on BC such that ad is perpendicular to BC prove that angle BAD = angle CAD
Answers
Given : ABC is an isosceles triangle with AB = AC and D is a point on BC such that ad is perpendicular to BC
To find : Show that ∠BAD = ∠CAD
Solution:
AD ⊥ BC
=> ΔABD & ΔACD are right angle triangle
Applying Pythagorean theorem
BD² = AB² - AD²
AB = AC
=> BD² = AC² - AD²
AC² - AD² = CD²
=> BD² = CD²
=> BD = CD Eq 1
Compare ΔABD & ΔACD
AB = AC ( given)
BD = CD ( from Eq 1)
AD = AD ( common)
=> ΔABD ≅ ΔACD
=> ∠BAD = ∠CAD
QED
Hence proved
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Answer:
Step-by-step explanation:
Given : ABC is an isosceles triangle with AB = AC and D is a point on BC such that ad is perpendicular to BC
To find : Show that ∠BAD = ∠CAD
Solution:
AD ⊥ BC
=> ΔABD & ΔACD are right angle triangle
Applying Pythagorean theorem
BD² = AB² - AD²
AB = AC
=> BD² = AC² - AD²
AC² - AD² = CD²
=> BD² = CD²
=> BD = CD Eq 1
Compare ΔABD & ΔACD
AB = AC ( given)
BD = CD ( from Eq 1)
AD = AD ( common)
=> ΔABD ≅ ΔACD
=> ∠BAD = ∠CAD
QED
Hence proved