Question : Which of the following statements is FALSE?
Option 1: Two triangles are congruent if the size and shape of the triangles may or may not be equal.
Option 2: SAS and SSS are both conditions of congruency of triangles.
Option 3: If two angles and the included side of one triangle are equal to two angles and the included side of the other triangle, the triangles are congruent.
Option 4: If two triangles are congruent, one of them can be superimposed on the other triangle.
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Correct Answer: Two triangles are congruent if the size and shape of the triangles may or may not be equal.
Solution : Two triangles are congruent if they have the same shape and size. In other words, the corresponding angles and sides of the two triangles are equal. Congruent triangles are identical in shape and size. So, the FALSE statement is ''Two triangles are congruent if the size and shape of the triangles may or may not be equal''. Hence, the correct answer is ''Two triangles are congruent if the size and shape of the triangles may or may not be equal''.
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Question : What is the ASA congruence rule of triangles, where A and S represent the angle and side of the triangle respectively?
Option 1: Two triangles are said to be congruent if all three sides of both triangles are equal.
Option 2: Two triangles are said to be congruent if 2 angles and the included side of one triangle are equal to 2 angles and the included side of the other triangle.
Option 3: Two triangles are said to be congruent if 2 sides and the included angle of one triangle are equal to 2 sides and the included angle of the other triangle.
Option 4: Two triangles are said to be congruent if any pair of 2 angles and any 1 pair of sides of both triangles are equal.
Question : If $\triangle ABC$ and $\triangle DEF$ are congruent triangles, which of the following is FALSE?
Option 1: The ratio of AC to DF is 2 : 1.
Option 2: The perimeters of both the triangles are equal.
Option 3: AB = DE and BC = EF
Option 4: The ratio of the angles in both the triangles is the same.
Question : In $\triangle$ABC and $\triangle$PQR, AB = PQ and $\angle$B = $\angle$Q. The two triangles are congruent by SAS criteria if:
Option 1: BC = QR
Option 2: AC = PR
Option 3: AC = QR
Option 4: BC = PQ
Question : Three sides of two triangles are 4, 5, and 6 cm. Select the INCORRECT statement.
Option 1: The angle opposite to the greater side in those triangles will be greater.
Option 2: The area of the two triangles will be different.
Option 3: The two triangles are congruent.
Option 4: The two triangles are scalene triangles.
Question : Which of the following is a true statement?
Option 1: Two similar triangles are always congruent.
Option 2: Two similar triangles have equal areas.
Option 3: Two triangles are similar if their corresponding sides are proportional.
Option 4: Two polygons are similar if their corresponding sides are proportional.
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