Advertisements
Advertisements
प्रश्न
In the figure, RT = TS, ∠1 = 2∠2 and ∠4 = 2∠3. Prove that ΔRBT ≅ ΔSAT.
Advertisements
उत्तर
∠1 = 2∠2 and ∠4 = 2∠3
1 = 22 and 4 = 23∠1 = ∠4 ...(vertically opposite angles)
⇒ 2∠2 = 2∠3 or ∠2 = ∠3 ........(i)
∠R = ∠S = ...(since RT = TS and angle opposite to equal sides are equal)
⇒ ∠TRB = ∠TSA = .........(ii)
In ΔRBT and ΔSAT.
RT = TS
∠TRB = ∠TSA
∠RTB = ∠STA = ...(common)
Therefore, ΔRBT ≅ ΔSAT. ...(ASA criteria)
APPEARS IN
संबंधित प्रश्न
If ΔDEF ≅ ΔBCA, write the part(s) of ΔBCA that correspond to ∠F
Find the measure of each angle of an equilateral triangle.
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.
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 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 the figure, AC = AE, AB = AD and ∠BAD = ∠EAC. Prove that BC = DE.
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.
PQRS is a quadrilateral and T and U are points on PS and RS respectively such that PQ = RQ, ∠PQT = ∠RQU and ∠TQS = ∠UQS. Prove that QT = QU.
In triangles ABC and PQR, ∠A = ∠Q and ∠B = ∠R. Which side of ∆PQR should be equal to side AB of ∆ABC so that the two triangles are congruent? Give reason for your answer.
