Advertisements
Advertisements
प्रश्न
Prove that:
(i) ∆ ABC ≅ ∆ ADC
(ii) ∠B = ∠D
(iii) AC bisects angle DCB
Advertisements
उत्तर
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
संबंधित प्रश्न
Mark the correct alternative in each of the following:
If ABC ≅ ΔLKM, then side of ΔLKM equal to side AC of ΔABC is
In ΔTPQ, ∠T = 65°, ∠P = 95° which of the following is a true statement?
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.
In the adjacent figure, seg AD ≌ seg EC Which additional information is needed to show that ∆ ABD and ∆ EBC will be congruent by A-A-S test?
If the following pair of the triangle is congruent? state the condition of congruency:
In ΔABC and ΔPQR, BC = QR, ∠A = 90°, ∠C = ∠R = 40° and ∠Q = 50°.
The following figure shown a triangle ABC in which AB = AC. M is a point on AB and N is a point on AC such that BM = CN.
Prove that:
State, whether the pairs of triangles given in the following figures are congruent or not:
In ΔABC and ΔPQR and, AB = PQ, BC = QR and CB and RQ are extended to X and Y respectively and ∠ABX = ∠PQY. = Prove that ΔABC ≅ ΔPQR.
In a triangle ABC, if D is midpoint of BC; AD is produced upto E such as DE = AD, then prove that:
a. DABD andDECD are congruent.
b. AB = EC
c. AB is parallel to EC
The congruent figures super impose each other completely.
