Exercise 8.3
1. In following pairs of triangles, find the pairs which are congruent? Also, write the criterion of congruence.
(i)
Solution:
Let's analyze ΔABC and ΔRPQ:
AB =
∠B = ∠
∠C = ∠
Therefore, ΔABC and ΔRPQ are congruent by
(ii)
Solution:
Let's analyze ΔABD and ΔCDB:
BD =
∠ABD = ∠
∠DBC = ∠
Therefore, ΔABD and ΔCDB are congruent by
(iii)
Solution:
Let's analyze ΔABQ and ΔCDQ:
AB =
∠BAQ = ∠
AQ =
Therefore, ΔABQ ≅ ΔCDQ by
(iv)
Solution:
Let's analyze ΔABC and ΔDEF:
∠A =
∠B =
∠C =
Similarly in ΔDEF:
∠D =
∠E =
∠F =
Although all angles are equal: {.reveal(when="blank-5")}• ∠A = ∠D = 70° {.reveal(when="blank-5")}• ∠B = ∠E = 50° {.reveal(when="blank-5")}• ∠C = ∠F = 60°
Therefore, the triangles are
2. In the adjacent figure: (i) Are ΔABC and ΔDCB congruent? (ii) Are ΔAOB congruent to ΔDOC? Also identify the relation between corresponding elements and give reason for your answer.
(i)
Solution:
Let's analyze both pairs of triangles:
In ΔABC and ΔDCB: ∠BAC = ∠
∠ACB = ∠
AC =
Therefore, ΔABC and ΔDCB are congruent by
(ii)
In ΔAOB and ΔDOC:
AO =
BO =
∠AOB =
Therefore, ΔAOB ≅ ΔDOC by
The corresponding elements are:
• AO =
• BO =
• ∠AOB =
• ∠OAB =
• ∠OBA =
This congruence proves that O is equidistant from points A, B, C, and D