Q4 of 70 Page 131

In □ ABCD, A—P—D, B—Q—C. If AB ∥ PQ and PQ || DC, prove that

AP X QC = PD X BQ.


Given: In □ ABCD, A—P—D, B—Q—C, ∥ and


To prove: AP×QC = PD×BQ


Proof: ∥ and


∴ ∥ ∥


So, , , are three ∥ linesand and are their transversal


∴


(∵ if three or more than three ∥ lines are intercepted by two transversal, the segments cut off on the transversal between the same parallel lines are proportional)


∴ AP × QC = PD × BQ hence proved


More from this chapter

All 70 →
2

□ ABCD is a parallelogram. Prove that ABD and BDC are similar.

 3

In □ABCD, M and N are the mid-points of and . If ∥ prove that ∥

 5

In Δ ABC, the bisector of ∠ A intersects BC in D. The bisector of ∠ADB intersects AB in F and the bisector of ∠ ADC intersects in E. Prove that AF X AB X CE = AE × AC × BF.

 6

In Δ ABC, Δ PQR and ΔXYZ correspondences ABC ↔ PQR, PQR ↔ XYZ are similarity. Prove that ABC ↔ XYZ is similarity.