Let ABC be a triangle with∠A = 90º and AB = AC. Let D and E be points on the segment BC such that BD : DE: EC = 3 : 5: 4.

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Let ABC be a triangle with∠A = 90º and AB = AC. Let D and E be points on the segment BC such that BD : DE: EC = 3 : 5: 4.

Let ABC be a triangle with∠A = 90⁰ and AB = AC. Let D and E be points on the segment BC such that BD : DE: EC = 3 : 5: 4. Prove that ∠DAE = 45⁰

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Salim Ahmed Kawsar · Answer 1 · Feb 05, 2023 15:29:48

Rotating the conguraiton about A by 90^0, the point B goes to the point C. Let P denote the image of the point D under this rotation. Then CP = BD and ∠ACP = ∠ABC = 45⁰, so ECP is a right-angled triangle with CE : CP = 4 : 3. Hence PE = ED. It follows that ADEP is a kite with AP = AD and PE = ED. Therefore AE is the angular bisector of ∠PAD. This implies that ∠DAE = ∠PAD/2 = 45⁰.

Let ABC be a triangle with∠A = 90º and AB = AC. Let D and E be points on the segment BC such that BD : DE: EC = 3 : 5: 4.

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