Page 6 - ln1

AB = PQ (Given)
∠ABC = ∠PQR [From Equation (2)]
BC = QR (Given)
∴ ΔABC ≅ ΔPQR (By SAS congruence rule)

Question 3
AD is an altitude of an isosceles △ABC in which AB = AC. Show that
(i) AD bisects BC,
(ii) AD bisects ∠A.

(i) Based on the △ BAD and △ CAD
o
We know that AD is the altitude so the angle is 90
o
So we get∠ ADB = ∠ ADC = 90
It is given that AB = AC and we know that AD is common.
Based on the RHS Congruence Criterion we get
△ BAD ≅△ CAD
So we get BD = CD (c. p. c. t)
Therefore, it is proved that AD bisects BC.
(ii) We also know that ∠ BAD = ∠ CAD (c. p. c. t)
Therefore, it is proved that AD bisects ∠ A.

Question 4 In the given figure, BE and CF are two equal altitudes of △ABC. Show
that
(i) △ABE ≅△ACF,
(ii) AB = AC.

(i) Based on the △ ABE and △ ACF
We know that
o
∠ AEB = ∠ AFC = 90
It is given that BE = CF
From the figure we know that ∠ A is common for both ∠ BAE and ∠ CAF