Q5 of 49 Page 21

Given : In trapezium PQRS, side PQ || side SR, AR = 5AP, AS = 5AQ then prove that, SR = 5PQ

Given that, AR = 5AP and AS = 5AQ

⇒ = 5 ………(1)


And = 5……….(2)


⇒


And, ∠ SAR≅ ∠ QAP …… (opposite angles)


⇒ Δ SAR ~ Δ QAP …………(SAS Test of similarity)


⇒ (corresponding sides are proportional)


But, = 5


⇒ = 5


⇒ SR = 5PQ


More from this chapter

All 49 →
3

As shown in figure 1.57, two poles of height 8 m and 4 m are perpendicular to the ground. If the length of shadow of smaller pole due to sunlight is 6 m then how long will be the shadow of the bigger pole at the same time?

 4

In ΔABC, AP ⊥ BC, BQ ⊥ AC B- P-C, A-Q - C then prove that, ΔCPA ~ ΔCQB. If AP = 7, BQ = 8, BC = 12 then find AC.

 6

In trapezium ABCD, (Figure 1.60) side AB || side DC, diagonals AC and BD intersect in point O. If AB = 20, DC = 6, OB = 15 then find OD.

 7

□ ABCD is a parallelogram point E is on side BC. Line DE intersects ray AB in point T. Prove that DE × BE = CE × TE.