Question

[nguyễn thị nga]

Cho ∆ABC co AB=3cm, AC=4cm, DC=5cm, DE la tia phan giac cua ABC(E€AC)tren tia doi cua tia BC lay diem Q sao cho DQ=3cm

∆ABC la ∆ gi? Vi sao?

AQ song song voi BE

Goi I la hinh chieu cua A tren BC ke tia Qx song song voi AB tren tia Qx lay diem K sao cho QI=QK, chung minh 3 diem A,C,K thang hang

Giup minh voi!

Answer 1

[Nguyễn Phương Uyên]

tu ke hinh

a, AB = 3cm (gt) => AB² = 3² = 9 cm

AC = 4cm (gt) => AC² = 4² = 16 cm

=> AB² + AC² = 9 + 15 = 25 cm

BC = cm (gt) => BC² = 5² = 25 cm

=> BC² = AB² + AC²

=> tam giac ABC vuong tai A (dinh li Pytago dao)

b, AB = 3cm (gt); BQ = 3cm (Gt)

=> AB = BQ 

=> tam giac ABQ can tai B (dn)

=> goc BAQ = (180 - goc ABQ) : 2    (1)

co goc ABQ + ABC = 180 (kb)

=> goc ABC = 180 - goc ABQ

BE la phan giac cua goc ABC (gt) => goc EBA = goc ABC : 2 (dn)

=> goc EBA = (180 - goc ABQ) : 2 (2)

(1)(2) => goc EBA = goc BAQ ma 2 goc nay so le trong

=> EB // AQ (dl)

c, co tam giac BAQ can tai B (cau b)

=> goc BAQ = goc BQA (dl)

Qx // AB => goc BAQ = goc AQK (slt)

=> goc BQA = goc AQK (tcbc)

xet tam giac AQI va tam giac AQK co : AQ chung

QI = QK (gt)0

=> tam giac AQI = tam giac AQK (c - g - c)

=> goc AIQ = goc AKQ (dn)

goc AIQ = 90 do I la hinh chieu cua A (gt)

=> goc AKQ = 90 

co goc AKQ + goc BAC = goc CAK ma goc BAC = 90 do tam giac ABC vuong tai A (cau a)

=> goc CAK = 180

=> C; A; K  thang hang