Exercise 8.1
1. Decide whether the SSS congruence is true with the following figures. Give reasons
Solution:
(i)
Let's check if SSS congruence criterion is satisfied:
Given triangles ∆NBE and ∆ARC have:
AC = BR (marked with
CR = NB (marked with
AR and NE are not marked
Since all three pairs of sides are not equal:
SSS congruence is
Therefore, ∆NBE is not
(ii)
Let's check if SSS congruence criterion is satisfied:
Given triangles ∆LSD and ∆LAD have:
LA =
LS ≠
LD =
Since all three pairs of sides are not equal: SSS congruence is
Therefore, ∆LSD
For the following congruent triangles, find the pairs of corresponding angles.
Solution:
(i)
Let's find the corresponding angles in congruent triangles:
Given ∆PTQ and ∆RSQ are congruent with:
PQ =
PT =
QT =
∠P = ∠
∠TQP = ∠
∠T = ∠
(ii)
Let's find the corresponding angles in congruent triangles:
Given ∆POQ and ∆ROS are congruent with:
PO =
OQ =
PQ =
∠ROS = ∠
∠R = ∠
∠S = ∠
3. In adjacent figure, choose the correct answer!
Solution:
Let's determine which option is correct:
Given quadrilateral PQRS with:
PR = SQ =
PQ is
PS = RQ =
Since all corresponding sides are equal:
Option
Therefore, ΔPQR ≅ ΔPQS by SSS criterion
4. In the figure given below, AB = DC and AC = DB. Is ΔABC ≅ ΔDCB.
Solution:
Let's check if the triangles are congruent:
Given that:
AB =
AC =
Comparing ∆ABC and ∆DCB: AB =
BC is
AC =
Since all three pairs of sides are equal: ∆ABC ≅ ∆DCB by SSS criterion