in a right angled triangle, if a perpendicular is drawn from the
right angle to the hypotemuse, the triangles formed are similar
to the whole triangle and to one another.
Answers
Step-by-step explanation:
△ABC right angled at B and ⊥ from B intersecting AC at D(BD⊥AC)
In△ADB&△ABC
∠A=∠A(common)
∠ADB=∠ABC{ Each 90
∘
}
△ADB∼△ABC{ By AA Similarity criterion} -(1)
Similarly,
In△BDC&△ABC
∠C=∠C{ common}
∠BDC=∠ABC{ Each 90
∘
}
△BDC∼△ABC{ By AA Similarity Criterion} -(2)
from(1)&(2)
△ADB∼△ABC&△BDC∼△ABC
If one △le is similar to another △le,and second△le is similar, to the third △le,then first & third △le are similar.
△ADB∼△BDC
solution
Step-by-step explanation:
Answer
△ABC right angled at B and ⊥ from B intersecting AC at D(BD⊥AC)
In△ADB&△ABC
∠A=∠A(common)
∠ADB=∠ABC{ Each 90
∘
}
△ADB∼△ABC{ By AA Similarity criterion} -(1)
Similarly,
In△BDC&△ABC
∠C=∠C{ common}
∠BDC=∠ABC{ Each 90
∘
}
△BDC∼△ABC{ By AA Similarity Criterion} -(2)
from(1)&(2)
△ADB∼△ABC&△BDC∼△ABC
If one △le is similar to another △le,and second△le is similar, to the third △le,then first & third △le are similar.
△ADB∼△BDC