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 ∠E
In triangles ABC and PQR, if ∠A = ∠R, ∠B = ∠P and AB = RP, then which one of the following congruence conditions applies:
Which of the following is not a criterion for congruence of triangles?
Observe the information shown in pair of triangle given below. State the test by which the two triangles are congruent. Write the remaining congruent parts of the triangles.
From the information shown in the figure,
In ΔABC and ΔPQR
∠ABC ≅ ∠PQR
seg BC ≅ seg QR
∠ACB ≅ ∠PRQ
∴ ΔABC ≅ ΔPQR ...`square` test
∴ ∠BAC ≅ `square` ...corresponding angles of congruent triangles.
`{:("seg AB" ≅ square),("and" square ≅ "seg PR"):}}` ...corresponding sides of congruent triangles
In the given figure, ∠P ≅ ∠R seg, PQ ≅ seg RQ. Prove that, ΔPQT ≅ ΔRQS.
In a triangle, ABC, AB = BC, AD is perpendicular to side BC and CE is perpendicular to side AB. Prove that: AD = CE.
State, whether the pairs of triangles given in the following figures are congruent or not:
In the given figure, prove that:
(i) ∆ ACB ≅ ∆ ECD
(ii) AB = ED
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.
ABCD is a quadrilateral in which AB = BC and AD = CD. Show that BD bisects both the angles ABC and ADC.
