Advertisements
Advertisements
प्रश्न
In the figure, ∠BCD = ∠ADC and ∠ACB =∠BDA. Prove that AD = BC and ∠A = ∠B.
Advertisements
उत्तर
∠BCD = ∠ADC
∠ACB = ∠BDA
∠BCD + ∠ACB = ∠ADC + ∠BDA
⇒ ∠ACD = ∠BDCACD = BDC
In ΔACD and ΔBCD
∠ACD =∠BDCACD = BDC
∠ADC = ∠BCD
ADC = BCD
CD = CD
Therefore, ΔACD ≅ ΔBCD ...(ASA criteria)
Hence, AD = BC and ∠A = ∠B.
APPEARS IN
संबंधित प्रश्न
From the information shown in the figure, state the test assuring the congruence of ΔABC and ΔPQR. Write the remaining congruent parts of the triangles.
In the pair of triangles given below, the parts shown by identical marks are congruent. State the test and the one-to-one correspondence of vertices by which the triangles in the pair are congruent, the remaining congruent parts.
If the following pair of the triangle is congruent? state the condition of congruency :
In ΔABC and ΔDEF, ∠B = ∠E = 90o; AC = DF and BC = EF.
Which of the following pairs of triangles are congruent? Give reasons
ΔABC;(AB = 5cm,BC = 7cm,CA = 9cm);
ΔKLM;(KL = 7cm,LM = 5cm,KM = 9cm).
In the figure, ∠CPD = ∠BPD and AD is the bisector of ∠BAC. Prove that ΔCAP ≅ ΔBAP and CP = BP.
In the figure, BM and DN are both perpendiculars on AC and BM = DN. Prove that AC bisects BD.
In ΔPQR, LM = MN, QM = MR and ML and MN are perpendiculars on PQ and PR respectively. Prove that PQ = PR.
AD and BE are altitudes of an isosceles triangle ABC with AC = BC. Prove that AE = BD.
ΔABC is isosceles with AB = AC. BD and CE are two medians of the triangle. Prove that BD = CE.
In the given figure, AB = DB and AC = DC. Find the values of x and y.
