1) Assertion : In the adjoining figure, X and Y are respectively two points on equal sides AB and AC of ΔABC such that AX = AY then CX = BY.
Reason: If two sides and the included angle of one triangle are equal to two sides and the included angle of the other triangle, then the two triangles are congruent
a) both Assertion and reason are correct and reason is correct explanation for Assertion.
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is true but reason is false.
d) both Assertion and reason are false.
Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion.
2) Assertion : In the given figure, BO and CO are the bisectors of ∠B and ∠C respectively. If ∠A = 50° then ∠BOC = 115°
Reason: The sum of all the interior angles of a triangle is 180°
a) both Assertion and reason are correct and reason is correct explanation for Assertion.
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is true but reason is false.
d) both Assertion and reason are false.
Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion.
3) Assertion: Two angles measures a – 60° and 123º – 2a. If each one is opposite to equal sides of an isosceles triangle, then the value of a is 61°.
Reason: Sides opposite to equal angles of a triangle are equal.
a) both Assertion and reason are correct and reason is correct explanation for Assertion.
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is true but reason is false.
d) both Assertion and reason are false.
Ans: b) both Assertion and reason are correct but reason is not correct explanation for Assertion.
4) Assertion: Assertion : In ΔABC, ∠C = ∠A, BC = 4 cm and AC = 5 cm. Then, AB = 4 cm
Reason: In a triangle, angles opposite to two equal sides are equal.
a) both Assertion and reason are correct and reason is correct explanation for Assertion.
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is true but reason is false.
d) both Assertion and reason are false.
Ans: b) both Assertion and reason are correct but reason is not correct explanation for Assertion.
5) Assertion: In ΔABC, BC = AB and B = 80°. Then, ∠A = 50°
Reason: In a triangle, angles opposite to two equal sides are equal
a) both Assertion and reason are correct and reason is correct explanation for Assertion.
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is true but reason is false.
d) both Assertion and reason are false.
Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion.
6) In ΔABC, D is the midpoint of BC. If DL I AB and DM I AC such that DL = DM, then BL = CM
Reason: If two angles and the included side of one triangle are equal to two angles
a) both Assertion and reason are correct and reason is correct explanation for Assertion.
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is true but reason is false.
d) both Assertion and reason are false.
Ans: b) both Assertion and reason are correct but reason is not correct explanation for Assertion.
7) Assertion : Sides opposite to equal angles of a triangle are equal.
Reason: Angles opposite to equal sides of a triangle are not equal.
a) both Assertion and reason are correct and reason is correct explanation for Assertion.
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is true but reason is false.
d) both Assertion and reason are false.
Ans: c) Assertion is correct but reason is false.
8) Assertion : In ΔABC, AB = AC and ∠B = 50°, then ∠C is 50°.
Reason: Angles opposite to equal sides of a triangle are equal
a) both Assertion and reason are correct and reason is correct explanation for Assertion.
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is true but reason is false.
d) both Assertion and reason are false.
Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion.
9) Assertion : ΔABC and ΔDBC are two isosceles triangles on the same base BC and vertices A and D are on the same side of BC. If AD is extended to intersect BC at E, then ΔABD ≅ ΔACD
Reason: If in two right triangles, hypotenuse and one side of a triangle are equal to the hypotenuse and one side of other triangle, then the two triangles are congruent.
a) both Assertion and reason are correct and reason is correct explanation for Assertion.
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is true but reason is false.
d) both Assertion and reason are false.
Ans: b) both Assertion and reason are correct but reason is not correct explanation for Assertion.
10) Assertion: In triangles ABC and PQR, ∠A = ∠P, ∠C = ∠R and AC = PR. The two triangles are congruent by ASA congruence.
Reason: If two angles and the included side of one triangle are equal to two angles and the included side of the other triangle, then the two triangles are congruent.
a) both Assertion and reason are correct and reason is correct explanation for Assertion.
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is true but reason is false.
d) both Assertion and reason are false.
Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion.
11) Assertion : In ΔABC and ΔPQR, AB = PQ, AC = PR and ∠BAC = ∠QPR then ΔABC ≅ ΔPQR
Reason: Both the triangles are congruent by SSS congruence.
a) both Assertion and reason are correct and reason is correct explanation for Assertion.
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is true but reason is false.
d) both Assertion and reason are false.
Ans: c) Assertion is true but reason is false.
12) Assertion: In the given figure, BE and CF are two equal altitudes of ΔABC then ΔABE ≅ ΔACF
Reason: If two angles and one side of one triangle are equal to two angles and the corresponding side of the other triangle, then the two triangles are congruent.
a) both Assertion and reason are correct and reason is correct explanation for Assertion.
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is true but reason is false.
d) both Assertion and reason are false.
Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion.
13) Assertion: In ABC, ∠A = ∠C and BC = 4 cm and AC = 3 cm then the length of side AB = 3 cm.
Reason: Sides opposite to equal angles of a triangle are equal.
a) both Assertion and reason are correct and reason is correct explanation for Assertion.
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is true but reason is false.
d) both Assertion and reason are false.
Ans: d) Assertion is true but reason is false.
14) Assertion : If the altitudes from two vertices of a triangle to the opposite sides are equal, then the triangle is an isosceles triangle.
Reason: If two angles and one side of one triangle are equal to two angles and the corresponding side of the other triangle, then the two triangles are congruent.
a) both Assertion and reason are correct and reason is correct explanation for Assertion.
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is true but reason is false.
d) both Assertion and reason are false.
Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion.
15)Assertion : In the given figure, ABCD is a quadrilateral in which AB || DC and P is the midpoint of BC. On producing, AP and DC meet at Q then DQ = DC + AB.
Reason: If two sides and the included angle of one triangle are equal to two sides
a) both Assertion and reason are correct and reason is correct explanation for Assertion.
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is true but reason is false.
d) both Assertion and reason are false.
Ans: b) both Assertion and reason are correct but reason is not correct explanation for Assertion.
16) Assertion: If three sides of one triangle are equal to the three sides of another triangle, then the two triangles are congruent
Reason: if AB/XY = BC/YZ = AC/XZ then ΔABC ~ΔXYZ.
a) both Assertion and reason are correct and reason is correct explanation for Assertion.
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is true but reason is false.
d) both Assertion and reason are false.
Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion.
17) Assertion: Two triangles are said to be congruent to each other if two angles and one side of one triangle are equal to two angles and one side of the other triangle.
Reason: ∠ B = ∠ Q, ∠ C = ∠ R and sides between ∠B and ∠C , ∠Q and ∠ R are equal to each other i.e. BC= QR. Hence, Δ ABC ≅ Δ PQR by AAS test
a) both Assertion and reason are correct and reason is correct explanation for Assertion.
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is true but reason is false.
d) both Assertion and reason are false.
Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion.
18) Assertion: In a Δ ABC, if AB = AC and ∠ B = 70°, ∠ A=40
Reason: sum of angle of triangle is 179°.
a) both Assertion and reason are correct and reason is correct explanation for Assertion.
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is true but reason is false.
d) both Assertion and reason are false.
Ans: c) Assertion is correct reason is false
19) Assertion: equilateral means unequal side.
Reason: all equilateral triangle are not isosceles.
a) both Assertion and reason are correct and reason is correct explanation for Assertion.
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is true but reason is false.
d) both Assertion and reason are false.
Ans: d) both Assertion and reason is false.
20) Assertion:equiangular means equal angles.
Reason: all isosceles triangle are equilangular
a) both Assertion and reason are correct and reason is correct explanation for Assertion.
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is true but reason is false.
d) both Assertion and reason are false.
Ans: c) Assertion is correct but reason is false.
21) Assertion: all equiangular triangles are isosceles.
Reason: all equilateral triangle are equiangular.
a) both Assertion and reason are correct and reason is correct explanation for Assertion.
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is true but reason is false.
d) both Assertion and reason are false.
Ans: b) both Assertion and reason are correct but reason is not correct explanation for Assertion
22) Assertion: all equilateral triangle are acute .
Reason: all acute triangles are equiangular
a) both Assertion and reason are correct and reason is correct explanation for Assertion.
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is true but reason is false.
d) both Assertion and reason are false.
Ans: c) Assertion is correct but reason is false
23) Assertion: All the sides of a square are of equal length.
Reason: all squares are congruent.
a) both Assertion and reason are correct and reason is correct explanation for Assertion.
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is true but reason is false.
d) both Assertion and reason are false.
Ans: c) Assertion is true but reason is false.
24) Assertion: In ΔABC,∠A=100° ,∠B=30°and ∠C=50° then AB>AC
Reason: the side opposite to largest angle is longest side of triangle .
a) both Assertion and reason are correct and reason is correct explanation for Assertion.
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is true but reason is false.
d) both Assertion and reason are false.
Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion.
25) Assertion: If length of the largest side of a triangle is 12 cm then other two sides of triangle can be 4.8 cm, 8.2cm
Reason: Sum of any two sides of a triangle is greater than the third side.
a) both Assertion and reason are correct and reason is correct explanation for Assertion.
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is true but reason is false.
d) both Assertion and reason are false.
Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion.
26) Assertion: In congruent triangle corresponding part are equal.
Reason: Two triangles are congruent if any two pairs of angle and pairs of corresponding sides are equal
a) both Assertion and reason are correct and reason is correct explanation for Assertion.
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is true but reason is false.
d) both Assertion and reason are false.
Ans: b) both Assertion and reason are correct but reason is not correct explanation for Assertion.
27) Assertion: the triangle in which two sides are equal is called isosceles triangle.
Reason:angle opposite to equal sides of an isosceles triangle are unequal.
a) both Assertion and reason are correct and reason is correct explanation for Assertion.
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is true but reason is false.
d) both Assertion and reason are false.
Ans: c) Assertion is correct but reason is false
28) Assertion: each angle of equilateral triangle is 60°
Reason: all angles are equal then it is called equilateral triangle.
a) both Assertion and reason are correct and reason is correct explanation for Assertion.
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is true but reason is false.
d) both Assertion and reason are false.
Ans: c) Assertion is correct but reason is false.
29) Assertion: Area of triangle = 1/2*base *height
Reason: area of right angled triangle = 1/2*product ofside making 90°
a) both Assertion and reason are correct and reason is correct explanation for Assertion.
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is true but reason is false.
d) both Assertion and reason are false.
Ans: b) both Assertion and reason are correct but reason is not correct explanation for Assertion.
30) Assertion: triangle consist three side ,three vertices.
Reason: triangle is open polygon
a) both Assertion and reason are correct and reason is correct explanation for Assertion.
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is true but reason is false.
d) both Assertion and reason are false.
Ans: c) Assertion is correct but reason is false.
31) Assertion: all the sides and angle are unequal are called scalene triangle.
Reason: scalene triangle has point of symmetry.
a) both Assertion and reason are correct and reason is correct explanation for Assertion.
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is true but reason is false.
d) both Assertion and reason are false.
Ans: c) Assertion is correct but reason is false.
32) assertion: A scalene triangle can be an obtuse-angled, acute-angled or right-angled triangle.
Reason: In a scalene obtuse triangle, the circumcenter will lie outside the triangle.
a) both Assertion and reason are correct and reason is correct explanation for Assertion.
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is true but reason is false.
d) both Assertion and reason are false.
Ans: b) both Assertion and reason are correct but reason is not correct explanation for Assertion.
33) Assertion: the area of the scalene triangle ABC with the sides 8 cm, 6 cm and 4 cm is 11.6cm^2
Reason: Area of triangle = √s(s−a)(s−b)(s−c)
a) both Assertion and reason are correct and reason is correct explanation for Assertion.
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is true but reason is false.
d) both Assertion and reason are false.
Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion.
34) Assertion: If the sides of a triangle are 9cm, 13 cm and 14cm. 36 its perimeter
Reason: perimeter of triangle= a+b+c
a) both Assertion and reason are correct and reason is correct explanation for Assertion.
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is true but reason is false.
d) both Assertion and reason are false.
Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion.
35) Assertion: Scalene triangle has all its three angles different in measures and obeys the angle sum property
Reason: the sum of the three interior angles equals 150 degree
a) both Assertion and reason are correct and reason is correct explanation for Assertion.
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is true but reason is false.
d) both Assertion and reason are false.
Ans: c) Assertion is correct but reason is false
36) Assertion:The altitude from the apex of an isosceles triangle bisects the base into two equal parts and also bisects its apex angle into two equal angles.
Reason: The altitude from the apex of an isosceles triangle divides the triangle into two congruent right-angled triangles.
a) both Assertion and reason are correct and reason is correct explanation for Assertion.
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is true but reason is false.
d) both Assertion and reason are false.
Ans: b) both Assertion and reason are correct but reason is not correct explanation for Assertion.
37) Assertion: The vertex of the triangle that is opposite is called the apex.
Reason: The angle at the apex of the triangle is called the vertex angle.
a) both Assertion and reason are correct and reason is correct explanation for Assertion.
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is true but reason is false.
d) both Assertion and reason are false.
Ans: b) both Assertion and reason are correct and reason is not correct explanation for Assertion.
38) Assertion: A straight line drawn from the apex to the base is known as the altitude of the triangle.
Reason: The length of this line is the height of the triangle.
a) both Assertion and reason are correct and reason is correct explanation for Assertion.
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is true but reason is false.
d) both Assertion and reason are false.
Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion.
39) assertion: In an equilateral triangle, median, angle bisector, and altitude for all sides are all the same.
Reason: The area of an equilateral triangle is √3a^2/ 4
a) both Assertion and reason are correct and reason is correct explanation for Assertion.
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is true but reason is false.
d) both Assertion and reason are false.
Ans: b) both Assertion and reason are correct and reason is not correct explanation for Assertion.
40) Assertion: If any of the incenter, orthocenter or centroid coincide with the circumcenter of a triangle, then it is called an equilateral trtriangle
Reason: height of equilateral triangle is √3a/4
a) both Assertion and reason are correct and reason is correct explanation for Assertion.
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is true but reason is false.
d) both Assertion and reason are false.
Ans: c) Assertion is correct but reason is false
41) Assertion: ABC is an equilateral triangle, then each angle equals to 60°
Reason: Equilateral triangle has all its sides equal and each angle measures 60°.
a) both Assertion and reason are correct and reason is correct explanation for Assertion.
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is true but reason is false.
d) both Assertion and reason are false.
Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion.
42) Assertion: In a right triangle, the longest side is hypotenus.
Reason: the side opposite to the largest angle will be the smallest one.
a) both Assertion and reason are correct and reason is correct explanation for Assertion.
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is true but reason is false.
d) both Assertion and reason are false.
Ans: c) Assertion is correct but reason is false.
43) Assertion: SSA is a criterion for the congruence of triangles.
Reason: SAS, ASA and SSS are not the criteria for the congruence of triangles.
a) both Assertion and reason are correct and reason is correct explanation for Assertion.
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is true but reason is false.
d) both Assertion and reason are false.
Ans: d) both Assertion and reason are false
44) Assertion: In triangles ABC and PQR, AB = AC, ∠C = ∠P and ∠B = ∠Q. The two triangles are isosceles but not congruent
Reason: two isosceles triangle are always congruent.
a) both Assertion and reason are correct and reason is correct explanation for Assertion.
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is true but reason is false.
d) both Assertion and reason are false.
Ans: c) Assertion is correct but reason is false
45) Assertion: In ∆ PQR, ∠R = ∠P and QR = 4 cm and PR = 5 cm. Then the length of PQ is 2 cm
Reason: the sides opposite to equal angle are unequal.
a) both Assertion and reason are correct and reason is correct explanation for Assertion.
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is true but reason is false.
d) both Assertion and reason are false.
Ans: d) both Assertion and reason are false
46) Assertion: Two sides of a triangle are of lengths 5 cm and 1.5 cm. The length of the third side of the triangle cannot be 3.4
Reason: the difference between the two sides of a triangle should be less than the third side.
a) both Assertion and reason are correct and reason is correct explanation for Assertion.
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is true but reason is false.
d) both Assertion and reason are false.
Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion.
47) Assertion: In ∆ ABC, AB = AC and ∠B = 50°. Then ∠C is equal to50°
Reason: the given triangle is an isosceles triangle, the angles opposite to the equal sides are also equal.
a) both Assertion and reason are correct and reason is correct explanation for Assertion.
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is true but reason is false.
d) both Assertion and reason are false.
Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion.
48) Assertion: two figures are congruent if they have same shape and same size.
Reason: two circles of different radii are congruent
a) both Assertion and reason are correct and reason is correct explanation for Assertion.
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is true but reason is false.
d) both Assertion and reason are false.
Ans: c) Assertion is correct but reason is false.
49) Assertion: D is a point on side BC of Δ ABC such that AD = AC then AB<AD
Reason: : In any triangle, the side opposite to the larger (greater) angle is smaller
a) both Assertion and reason are correct and reason is correct explanation for Assertion.
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is true but reason is false.
d) both Assertion and reason are false.
Ans: d) both Assertion and reason are false
50) Assertion: each angle of equilateral triangle is always 50°
Reason: equilateral triangle is always obtuse angled triangle.
a) both Assertion and reason are correct and reason is correct explanation for Assertion.
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is true but reason is false.
d) both Assertion and reason are false.
Ans: d) both Assertion and reason are false.
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