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Byju's Answer
Standard IX
Mathematics
Why SSA and AAA Congruency Rules Are Not Valid?
In ∆PQR ≅ ∆MN...
Question
In
∆
PQR
≅
∆
MNS then state all pair of congruent angles and sides.
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Solution
Given
:
∆
PQR
≅
△
MNS
T
hen
by
cpct
,
∠
P
≅
∠
M
,
∠
Q
≅
∠
N
,
∠
R
≅
∠
S
and
PQ
≅
MN
,
QR
≅
NS
,
PR
≅
MS
.
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≅
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If
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∆CDE and ∆PQR are congruent by the correspondence CDE ↔ RPQ. Write down the names of the pairs of congruent sides and angles.
Q.
Observe the information shown in pairs of triangles given below. State the test by which the two triangles are congruent. Write the remaining congruent parts of the triangles.
(i)
From the information shown in the figure,
in
∆
ABC and
∆
PQR
∠
ABC
≅
∠
PQR
seg BC
≅
seg QR
∠
ACB
≅
∠
PRQ
∴
∆
ABC
≅
∆
PQR .......
3243432
test
∴
∠
BAC
≅
3243432
.......corresponding angles of congruent triangles.
seg
AB
≅
1234
and
1234
≅
seg
PR
.
.
.
corresponding
sides
of
congruent
triangles
(ii)
From the information shown in the figure,
in
∆
PTQ and
∆
STR
seg PT
≅
seg ST
∠
PTQ
≅
∠
STR...... vertically opposite angles
∴
∆
PTQ
≅
∆
STR .......
3243432
test
∴
∠
TPQ
≅
1234
and
1234
≅
∠
TRS
.
.
.
corresponding
angles
of
congruent
triangles
seg PQ
≅
3243432
corresponding sides of congruent triangles
