Question

In ∆ABC, PQ || BC and in ∆ACD, QR || CD.
(i) Prove that AAQR ~ AACD.
(ii) If AP=2, PB=5, AQ=3, QR=5, calculate
the lengths of QC and CD.
​

Answer 1

Step-by-step explanation:

(i)In ∆ABD PR || BD

therefore

aAQR~aACD (CORRESPONDING ANGLES)

(ii)AP/PB=AQ/QC (BPT)

2/5=3/QC

2*QC=5*3

QC=15/2

QC=7.5

IN ∆AQR & ∆ACD

aAQR=aACD (FROM i)

aACR=aACD (COMMON ANGLE)

∆AQR ~ ∆ACD (AA TEST)

AQ/AC=QR/CD (c.s.s.t)

3/10.5=5/CD

3*CD=10.5*5

CD=52.5/3

CD=17.5