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!
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
