Advertisements
Advertisements
प्रश्न
Sides, AB, BC and the median AD of ΔABC are equal to the two sides PQ, QR and the median PM of ΔPQR. Prove that ΔABC ≅ ΔPQR.
Advertisements
उत्तर
In ΔABC and ΔPQR
BC = QR
AD and PM are medians of BC and QR respectively
⇒ BD = DC = QM = MR
In ΔABD and ΔPQM
AB = PQ
D = PM
BD = QM
Therefore, ΔABD ≅ ΔPQMABD PQM ...(SSS criteria)
Hence, ∠B = ∠Q
Now in ΔABC and ΔPQR
AB = PQ
BC = QR
∠B = ∠Q
Therefore, ΔABC ≅ ΔPQRABC PQR. ...(SAS criteria)
APPEARS IN
संबंधित प्रश्न
In the given figure, if AB = AC and ∠B = ∠C. Prove that BQ = CP.
Mark the correct alternative in each of the following:
If ABC ≅ ΔLKM, then side of ΔLKM equal to side AC of ΔABC is
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.
On the sides AB and AC of triangle ABC, equilateral triangle ABD and ACE are drawn. Prove that:
- ∠CAD = ∠BAE
- CD = BE
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: ΔAMC≅ ΔANB
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 ΔPQR, LM = MN, QM = MR and ML and MN are perpendiculars on PQ and PR respectively. Prove that PQ = PR.
In the figure, AC = AE, AB = AD and ∠BAD = ∠EAC. Prove that BC = DE.
In ΔABC, AB = AC. D is a point in the interior of the triangle such that ∠DBC = ∠DCB. Prove that AD bisects ∠BAC of ΔABC.
