Q4 of 45 Page 49

In figure 3.59, point D and E are on side BC of ΔABD, such that BD = CE and AD = AE. Show that ΔABD ≅ ΔACE.

Given: BD = CE


AD = AE


To Prove: ΔABD ≅ ΔACE


Proof:


In ΔADE


AD = AE [given]


⇒ ∠ADE = ∠AED [angles opposite to equal sides are equal] ……(1)


Subtracting 180° from (1)


⇒ 180° - ∠ADE = 180° - ∠AED


⇒ ∠ADB = ∠AEC (2)


In ΔABD and ΔACE


BD = CE [Given]


AD = AE [Given]


∠ADB = ∠AEC [from (2)]


∴ By SAS congruency test


ΔABD ≅ ΔACE


More from this chapter

All 45 →
2

ΔABC is isosceles in which AB = AC. seg BD and seg CE are medians. Show that BD = CE.

 3

In ΔPQR, If PQ>PR and bisectors of ∠Q and ∠R intersect at S. Show that SQ>SR.

 5

In figure 3.60, point S is any point on side QR of ΔPQR.

Prove that: PQ + QR + RP > 2PS


 6

In figure 3.61, bisector of ∠BAC intersects side BC at point D.

Prove that AB > BD