Advertisements
Advertisements
Question
Prove that:
(i) ∆ ABC ≅ ∆ ADC
(ii) ∠B = ∠D
(iii) AC bisects angle DCB
Advertisements
Solution
Given: In the figure,
AB = AD, CB = CD
To prove: Δ ABC ≅ Δ ADC
∠B = ∠D
AC bisects angle DCB
Proof: In Δ ABC and Δ ADC,
AC = AC .............(common)
AB = AD .............(given)
CB = CD .............(given)
(i) ∴ Δ ABC ≅ Δ ADC .................(SSS aciom)
(ii) ∴ ∠B = D .................(c.p.c.t.)
∠BCA = ∠DCA
(iii) ∴ AC bisects ∠DCB
APPEARS IN
RELATED QUESTIONS
In Fig. 10.22, the sides BA and CA have been produced such that: BA = AD and CA = AE.
Prove that segment DE || BC.
In a ΔPQR, if PQ = QR and L, M and N are the mid-points of the sides PQ, QR and RP
respectively. Prove that: LN = MN.
Prove that the sum of three altitudes of a triangle is less than the sum of its sides.
If ΔABC ≅ ΔABC is isosceles with
In ΔPQR ≅ ΔEFD then ED =
In the pair of triangles in the following figure, parts bearing identical marks are congruent. State the test and the correspondence of vertices by the triangle in pairs is congruent.
State, whether the pairs of triangles given in the following figures are congruent or not:
Which of the following pairs of triangles are congruent? Give reasons
ΔABC;(AB = 8cm,BC = 6cm,∠B = 100°);
ΔPQR;(PQ = 8cm,RP = 5cm,∠Q = 100°).
Prove that in an isosceles triangle the altitude from the vertex will bisect the base.
In triangles ABC and PQR, ∠A = ∠Q and ∠B = ∠R. Which side of ∆PQR should be equal to side BC of ∆ABC so that the two triangles are congruent? Give reason for your answer.
