CBSE Class 7 Mathematics Geometric Twins MCQs Set 04

Question. If ΔABC and ΔXYZ have AB = XY, AC = XZ, and ∠A = ∠X, they are congruent by which condition?
(a) SSS
(b) ASA
(c) SAS
(d) AAS

Answer: C

Question. When we have two sides and a non-included angle equal (SSA condition), congruence is
(a) Guaranteed always
(b) Guaranteed only for 90° angle
(c) Not guaranteed always
(d) Guaranteed for equilateral triangles

Answer: C

Question. In the construction of SSA triangle (base 6 cm, angle 30°, side 4 cm), the arc intersects the line at two points, R and S. This means we get two triangles (ΔPQR and ΔPQS) that are
(a) Always similar
(b) Non-congruent
(c) Always congruent
(d) Right-angled

Answer: B

Question. The ASA condition for congruence means that two angles and which side must be equal?
(a) Non-included side
(b) Shortest side
(c) Included side
(d) Longest side

Answer: C

Question. If ΔAOB ≅ ΔDOC, the lengths of sides AB and DC are
(a) Different
(b) Equal
(c) Proportional
(d) Double

Answer: B

Question. If AB and CD are parallel lines, and AC is a transversal, the alternate angles ∠BAC and ∠DCA are
(a) Complementary
(b) Supplementary
(c) Equal
(d) Vertically opposite

Answer: C

Question. The AAS condition for congruence involves two angles and a side that is
(a) Included between the angles
(b) Opposite to the smallest angle
(c) Non-included
(d) The hypotenuse

Answer: C

Question. If ΔABC has ∠A = 35° and ∠C = 75°, then ∠B is found by subtracting 35° + 75° from 180°. ∠B is
(a) 110°
(b) 70°
(c) 80°
(d) 50°

Answer: B

Question. Congruence is a powerful tool used to discover properties of figures, such as which type of triangle?
(a) Scalene triangles
(b) Isosceles triangles
(c) Obtuse triangles
(d) Right triangles only

Answer: B

Question. In an isosceles triangle, the angles opposite to the equal sides are
(a) Not equal
(b) Always 90°
(c) Equal
(d) Complementary

Answer: C

Question. If ΔABC is isosceles with AB = AC, and we construct altitude AD, then ΔADB and ΔADC are congruent by which condition?
(a) SAS
(b) ASA
(c) SSS
(d) RHS

Answer: D

Question. If ΔADB ≅ ΔADC, this proves that ∠B and ∠C are equal because they are
(a) Base angles
(b) Corresponding parts of congruent triangles
(c) Alternate angles
(d) Adjacent angles

Answer: B

Question. If ΔABC is an equilateral triangle, all three sides must be
(a) Different lengths
(b) Equal lengths
(c) Only two equal lengths
(d) Proportional lengths

Answer: B

Question. Congruent triangles are widely used in designs, examples include the Louvre Museum, the Egyptian Pyramid of Giza, and
(a) Howrah Bridge or Rabindra Setu
(b) Eiffel Tower (Not in source)
(c) India Gate (Not in source)
(d) Taj Mahal (Not in source)

Answer: A

Question. If ΔAIR ≅ ΔFLY, then side IR corresponds to side
(a) FL
(b) LY
(c) FY
(d) AI

Answer: B

Question. If two triangles ΔABC and ΔDEF have AB = DE, BC = EF, and CA = DF, they are congruent by
(a) SAS
(b) ASA
(c) SSS
(d) AAS

Answer: C

Question. If ΔHEN ≅ ΔBIG, the vertex E corresponds to which vertex?
(a) B
(b) G
(c) I
(d) H

Answer: C

Question. For ΔABD and ΔCDB (in a rectangle), if we try to overlap A over C, B over B, and D over D, will the sides AB and CB necessarily overlap exactly?
(a) Yes, they must be equal
(b) No, they need not be equal
(c) Only if ABCD is a square
(d) Cannot say

Answer: B

Question. If ΔHEN is congruent to ΔBIG, which is a correct way to express this congruence?
(a) ΔEHN ≅ ΔGIB
(b) ΔBGI ≅ ΔHNE
(c) ΔNHE ≅ ΔGIB
(d) ΔENH ≅ ΔIGB

Answer: D

Question. If DF = DG and FE = GE in two triangles (ΔDFE and ΔDGE), and DE is the common side, what congruence condition is satisfied?
(a) SAS
(b) ASA
(c) SSS
(d) RHS

Answer: C