Class 9 Exam > Class 9 Notes > Mathematics (Maths) Class 9 > RS Aggarwal MCQs: Congruence of Triangles and Inequalities in a Triangle
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Page 1
Question:44
Which of the following is not a criterion for congruence of triangles?
a
SSA
b
SAS
c
ASA
d
SSS
Solution:
a
SSA
SSA is not a criterion for congruence of triangles.
Question:45
If AB = QR, BC = RP and CA = PQ, then which of the following holds?
a
?ABC ? ?PQR
b
?CBA ? ?PQR
c
?CAB ? ?PQR
d
?BCA ? ?PQR
Solution:
c
? CAB ? ? PQR
Page 2
Question:44
Which of the following is not a criterion for congruence of triangles?
a
SSA
b
SAS
c
ASA
d
SSS
Solution:
a
SSA
SSA is not a criterion for congruence of triangles.
Question:45
If AB = QR, BC = RP and CA = PQ, then which of the following holds?
a
?ABC ? ?PQR
b
?CBA ? ?PQR
c
?CAB ? ?PQR
d
?BCA ? ?PQR
Solution:
c
? CAB ? ? PQR
As,
AB = QR, given
BC = RP, given
CA = PQ given
? ? CAB ? ? PQR
Question:46
If ?ABC ? ?PQR then which of the following is not true?
a BC = PQ
b AC = PR
c BC = QR
d AB = PQ
Solution:
a
BC = PQ
If ? ABC ? ? PQR
, then
BC = QR
Hence, the correct answer is option a
.
Question:47
In ?ABC, AB = AC and ?B = 50°. Then, ?A = ?
a 40°
b 50°
c 80°
d 130°
Solution:
In ? ABC
, we have:
AB = AC
?B = 50°
Since ABC is an isosceles triangle, we have:
?C = ?B
?C = 50°
In triangle ABC, we have:
?A + ?B + ?C = 180° ? ?A +50 +50 = 180° ? ?A = 180°-100° ? ?A = 80°
Hence, the correct answer is option c
.
Question:48
In ?ABC, BC = AB and ?B = 80°. Then, ?A = ?
a 50°
b 40°
c 100°
d 80°
Solution:
Given: In ?ABC, BC = AB and ?B = 80°.
In ?ABC,
As, AB = BC
? ?A = ?C
Let ?A = ?C = x
Using angle sum property of a triangle,
?A + ?B + ?C = 180° ? x +80°+ x = 180° ? 2x = 180°-80° ? 2x = 100°
? x =
100°
2
? x = 50° ? ?A = 50°
Hence, the correct option is a
.
Question:49
In ?ABC, ?C = ?A, BC = 4 cm and AC = 5 cm. Then, AB = ?
a 4 cm
b 5 cm
c 8 cm
d 2.5 cm
Solution:
Page 3
Question:44
Which of the following is not a criterion for congruence of triangles?
a
SSA
b
SAS
c
ASA
d
SSS
Solution:
a
SSA
SSA is not a criterion for congruence of triangles.
Question:45
If AB = QR, BC = RP and CA = PQ, then which of the following holds?
a
?ABC ? ?PQR
b
?CBA ? ?PQR
c
?CAB ? ?PQR
d
?BCA ? ?PQR
Solution:
c
? CAB ? ? PQR
As,
AB = QR, given
BC = RP, given
CA = PQ given
? ? CAB ? ? PQR
Question:46
If ?ABC ? ?PQR then which of the following is not true?
a BC = PQ
b AC = PR
c BC = QR
d AB = PQ
Solution:
a
BC = PQ
If ? ABC ? ? PQR
, then
BC = QR
Hence, the correct answer is option a
.
Question:47
In ?ABC, AB = AC and ?B = 50°. Then, ?A = ?
a 40°
b 50°
c 80°
d 130°
Solution:
In ? ABC
, we have:
AB = AC
?B = 50°
Since ABC is an isosceles triangle, we have:
?C = ?B
?C = 50°
In triangle ABC, we have:
?A + ?B + ?C = 180° ? ?A +50 +50 = 180° ? ?A = 180°-100° ? ?A = 80°
Hence, the correct answer is option c
.
Question:48
In ?ABC, BC = AB and ?B = 80°. Then, ?A = ?
a 50°
b 40°
c 100°
d 80°
Solution:
Given: In ?ABC, BC = AB and ?B = 80°.
In ?ABC,
As, AB = BC
? ?A = ?C
Let ?A = ?C = x
Using angle sum property of a triangle,
?A + ?B + ?C = 180° ? x +80°+ x = 180° ? 2x = 180°-80° ? 2x = 100°
? x =
100°
2
? x = 50° ? ?A = 50°
Hence, the correct option is a
.
Question:49
In ?ABC, ?C = ?A, BC = 4 cm and AC = 5 cm. Then, AB = ?
a 4 cm
b 5 cm
c 8 cm
d 2.5 cm
Solution:
Given: In ?ABC, ?C = ?A, BC = 4 cm and AC = 5 cm.
In ?ABC,
As, ?C = ?A Given
Therefore, BC = AB
Sidesoppositetoequalangles.
? BC = AB = 4 cm
Hence, the correct option is a
.
Question:50
Two sides of a triangle are of length 4 cm and 2.5 cm. The length of the third side of the triangle cannot be
a
6 cm
b
6.5 cm
c
5.5 cm
d
6.3 cn
Solution:
Since, 4 + 2.5 = 6.5
So, 6.5 cm cannot be the third side of the triangle, as the sum of two sides of a triangle is always greater than the third side.
Hence, the correct option is b
.
Question:51
In ?ABC, if ?C > ?B, then
a BC > AC
b AB > AC
c AB > AC
d BC > AC
Solution:
b
AB > AC
In ? ABC
, we have:
?C > ?B
The side opposite to the greater angle is larger.
? AB > AC
Question:52
It is given that ?ABC ? ? FDE in which AB = 5 cm, ?B = 40°, ?A = 80° and FD = 5 cm. Then, which of the following is true?
a ?D = 60°
b ?E = 60°
c ?F = 60°
d
?D = 80°
Solution:
b
? ?E = 60°
? ABC ? ? FDE
AB = 5cm, ?B = 40°, ?A = 80°
and FD = 5cm
Then ?A + ?B + ?C = 180° ? 80°+40°+ ?C = 180° ? ?C = 60°Also, ?C = ?E
? ?E = 60°
Page 4
Question:44
Which of the following is not a criterion for congruence of triangles?
a
SSA
b
SAS
c
ASA
d
SSS
Solution:
a
SSA
SSA is not a criterion for congruence of triangles.
Question:45
If AB = QR, BC = RP and CA = PQ, then which of the following holds?
a
?ABC ? ?PQR
b
?CBA ? ?PQR
c
?CAB ? ?PQR
d
?BCA ? ?PQR
Solution:
c
? CAB ? ? PQR
As,
AB = QR, given
BC = RP, given
CA = PQ given
? ? CAB ? ? PQR
Question:46
If ?ABC ? ?PQR then which of the following is not true?
a BC = PQ
b AC = PR
c BC = QR
d AB = PQ
Solution:
a
BC = PQ
If ? ABC ? ? PQR
, then
BC = QR
Hence, the correct answer is option a
.
Question:47
In ?ABC, AB = AC and ?B = 50°. Then, ?A = ?
a 40°
b 50°
c 80°
d 130°
Solution:
In ? ABC
, we have:
AB = AC
?B = 50°
Since ABC is an isosceles triangle, we have:
?C = ?B
?C = 50°
In triangle ABC, we have:
?A + ?B + ?C = 180° ? ?A +50 +50 = 180° ? ?A = 180°-100° ? ?A = 80°
Hence, the correct answer is option c
.
Question:48
In ?ABC, BC = AB and ?B = 80°. Then, ?A = ?
a 50°
b 40°
c 100°
d 80°
Solution:
Given: In ?ABC, BC = AB and ?B = 80°.
In ?ABC,
As, AB = BC
? ?A = ?C
Let ?A = ?C = x
Using angle sum property of a triangle,
?A + ?B + ?C = 180° ? x +80°+ x = 180° ? 2x = 180°-80° ? 2x = 100°
? x =
100°
2
? x = 50° ? ?A = 50°
Hence, the correct option is a
.
Question:49
In ?ABC, ?C = ?A, BC = 4 cm and AC = 5 cm. Then, AB = ?
a 4 cm
b 5 cm
c 8 cm
d 2.5 cm
Solution:
Given: In ?ABC, ?C = ?A, BC = 4 cm and AC = 5 cm.
In ?ABC,
As, ?C = ?A Given
Therefore, BC = AB
Sidesoppositetoequalangles.
? BC = AB = 4 cm
Hence, the correct option is a
.
Question:50
Two sides of a triangle are of length 4 cm and 2.5 cm. The length of the third side of the triangle cannot be
a
6 cm
b
6.5 cm
c
5.5 cm
d
6.3 cn
Solution:
Since, 4 + 2.5 = 6.5
So, 6.5 cm cannot be the third side of the triangle, as the sum of two sides of a triangle is always greater than the third side.
Hence, the correct option is b
.
Question:51
In ?ABC, if ?C > ?B, then
a BC > AC
b AB > AC
c AB > AC
d BC > AC
Solution:
b
AB > AC
In ? ABC
, we have:
?C > ?B
The side opposite to the greater angle is larger.
? AB > AC
Question:52
It is given that ?ABC ? ? FDE in which AB = 5 cm, ?B = 40°, ?A = 80° and FD = 5 cm. Then, which of the following is true?
a ?D = 60°
b ?E = 60°
c ?F = 60°
d
?D = 80°
Solution:
b
? ?E = 60°
? ABC ? ? FDE
AB = 5cm, ?B = 40°, ?A = 80°
and FD = 5cm
Then ?A + ?B + ?C = 180° ? 80°+40°+ ?C = 180° ? ?C = 60°Also, ?C = ?E
? ?E = 60°
Question:53
In ?ABC, ?A = 40° and ?B = 60°. Then the longest side of ?ABC is
a BC
b AC
c AB
d cannot be determined
Solution:
c
AB
In triangle ABC, we have:
?A = 40°, ?B = 60°
...Given
Here, ?A + ?B + ?C = 180° ? 60°+40°+ ?C = 180° ? ?C = 80°
? The side opposite to ?C
, i.e., AB, is the longest side of triangle ABC.
Question:54
In the given figure, AB > AC. Then which of the following is true?
a
AB < AD
b
AB = AD
c
AB > AD
d
Cannot be determined
Solution:
c
AB > AD
AB > AC
is given.
? ?ACB > ?ABC
Now, ?ADB > ?ACD (exterior angle) ? ?ADB > ?ACB > ?ABC ? ?ADB > ?ABD ? AB > AD
Question:55
In the given figure, AB > AC. If BO and CO are the bisectors of ?B and ?C respectively, then
a
OB = OC
b
OB > OC
c
OB < OC
Solution:
b
OB > OC
AB >AC Given
? ?C > ?B
?
1
2
?C >
1
2
?B
? ?OCB > ?OBC
Given
? OB > OC
Question:56
In the given figure, AB = AC and OB = OC. Then, ?ABO : ?ACO = ?
a 1 : 1
b 2 : 1
c 1 : 2
d None of these
Page 5
Question:44
Which of the following is not a criterion for congruence of triangles?
a
SSA
b
SAS
c
ASA
d
SSS
Solution:
a
SSA
SSA is not a criterion for congruence of triangles.
Question:45
If AB = QR, BC = RP and CA = PQ, then which of the following holds?
a
?ABC ? ?PQR
b
?CBA ? ?PQR
c
?CAB ? ?PQR
d
?BCA ? ?PQR
Solution:
c
? CAB ? ? PQR
As,
AB = QR, given
BC = RP, given
CA = PQ given
? ? CAB ? ? PQR
Question:46
If ?ABC ? ?PQR then which of the following is not true?
a BC = PQ
b AC = PR
c BC = QR
d AB = PQ
Solution:
a
BC = PQ
If ? ABC ? ? PQR
, then
BC = QR
Hence, the correct answer is option a
.
Question:47
In ?ABC, AB = AC and ?B = 50°. Then, ?A = ?
a 40°
b 50°
c 80°
d 130°
Solution:
In ? ABC
, we have:
AB = AC
?B = 50°
Since ABC is an isosceles triangle, we have:
?C = ?B
?C = 50°
In triangle ABC, we have:
?A + ?B + ?C = 180° ? ?A +50 +50 = 180° ? ?A = 180°-100° ? ?A = 80°
Hence, the correct answer is option c
.
Question:48
In ?ABC, BC = AB and ?B = 80°. Then, ?A = ?
a 50°
b 40°
c 100°
d 80°
Solution:
Given: In ?ABC, BC = AB and ?B = 80°.
In ?ABC,
As, AB = BC
? ?A = ?C
Let ?A = ?C = x
Using angle sum property of a triangle,
?A + ?B + ?C = 180° ? x +80°+ x = 180° ? 2x = 180°-80° ? 2x = 100°
? x =
100°
2
? x = 50° ? ?A = 50°
Hence, the correct option is a
.
Question:49
In ?ABC, ?C = ?A, BC = 4 cm and AC = 5 cm. Then, AB = ?
a 4 cm
b 5 cm
c 8 cm
d 2.5 cm
Solution:
Given: In ?ABC, ?C = ?A, BC = 4 cm and AC = 5 cm.
In ?ABC,
As, ?C = ?A Given
Therefore, BC = AB
Sidesoppositetoequalangles.
? BC = AB = 4 cm
Hence, the correct option is a
.
Question:50
Two sides of a triangle are of length 4 cm and 2.5 cm. The length of the third side of the triangle cannot be
a
6 cm
b
6.5 cm
c
5.5 cm
d
6.3 cn
Solution:
Since, 4 + 2.5 = 6.5
So, 6.5 cm cannot be the third side of the triangle, as the sum of two sides of a triangle is always greater than the third side.
Hence, the correct option is b
.
Question:51
In ?ABC, if ?C > ?B, then
a BC > AC
b AB > AC
c AB > AC
d BC > AC
Solution:
b
AB > AC
In ? ABC
, we have:
?C > ?B
The side opposite to the greater angle is larger.
? AB > AC
Question:52
It is given that ?ABC ? ? FDE in which AB = 5 cm, ?B = 40°, ?A = 80° and FD = 5 cm. Then, which of the following is true?
a ?D = 60°
b ?E = 60°
c ?F = 60°
d
?D = 80°
Solution:
b
? ?E = 60°
? ABC ? ? FDE
AB = 5cm, ?B = 40°, ?A = 80°
and FD = 5cm
Then ?A + ?B + ?C = 180° ? 80°+40°+ ?C = 180° ? ?C = 60°Also, ?C = ?E
? ?E = 60°
Question:53
In ?ABC, ?A = 40° and ?B = 60°. Then the longest side of ?ABC is
a BC
b AC
c AB
d cannot be determined
Solution:
c
AB
In triangle ABC, we have:
?A = 40°, ?B = 60°
...Given
Here, ?A + ?B + ?C = 180° ? 60°+40°+ ?C = 180° ? ?C = 80°
? The side opposite to ?C
, i.e., AB, is the longest side of triangle ABC.
Question:54
In the given figure, AB > AC. Then which of the following is true?
a
AB < AD
b
AB = AD
c
AB > AD
d
Cannot be determined
Solution:
c
AB > AD
AB > AC
is given.
? ?ACB > ?ABC
Now, ?ADB > ?ACD (exterior angle) ? ?ADB > ?ACB > ?ABC ? ?ADB > ?ABD ? AB > AD
Question:55
In the given figure, AB > AC. If BO and CO are the bisectors of ?B and ?C respectively, then
a
OB = OC
b
OB > OC
c
OB < OC
Solution:
b
OB > OC
AB >AC Given
? ?C > ?B
?
1
2
?C >
1
2
?B
? ?OCB > ?OBC
Given
? OB > OC
Question:56
In the given figure, AB = AC and OB = OC. Then, ?ABO : ?ACO = ?
a 1 : 1
b 2 : 1
c 1 : 2
d None of these
Solution:
a
1:1
?In ? OAB and ? OAC, we have:
AB = AC (Given)OB = OC (Given) OA = OA (Common side)
Thus, ? OAB ? OAC (SSS criterion)
i.e., ?ABO = ?ACO
? ?ABO : ?ACO = 1 : 1
Question:57
If the altitudes from two vertices of a triangle to the opposite sides are equal, then the triangle is
a
equilateral
b
isosceles
c
scalene
d
right-angled
Solution:
b
isosceles
In ? ABC, BL ? AC.
CM ? AB such that BL = CM.
To prove: AB = AC
In ? ABL and ? ACM, BL = CM (Given) ?BAL = ?CAM (Common angle) ?ALB = ?AMC (Each 90°) ? ABL ? ? ACM (AAS criterion) ? AB = AC (CPCT)
Question:58
In ?ABC and ?DEF, it is given that AB = DE and BC = EF. In order that ?ABC ? ?DEF, we must have
a
?A = ?D
b ?B = ?E
c ?C = ?F
d none of these
Solution:
b
?B = ?E
In ? ABC and ? DEF, we have:
AB = DE Given
BC = EF Given
In order that ? ABC ? DEF
, we must have ?B = ?E
.
Question:59
In ?ABC and ?DEF, it is given that ?B = ?E and ?C = ?F. In order that ?ABC ? ?DEF, we must have
a AB = DF
b AC = DE
c BC = EF
d ?A = ?D
Solution:
In order that ? ABC ? ? DEF
, we must have BC = EF.
Hence, the correct answer is option
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