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.
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Correct Answer: The area of the two triangles will be different.
Solution : Let's check the options. Options 1: The angle opposite to the greater side in those triangles will be greater. It is correct. Option 2: The area of the two triangles will be different. It is incorrect. Triangles with the same sides will have the same area. Option 3: The two triangles are congruent. It is correct. Two triangles with the same sides also have the same angles. Option 4: The two triangles are scalene. It is correct. Hence, the correct answer is "The area of the two triangles will be different".
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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 : 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.
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.
Question : Let ABC and PQR be two congruent triangles such that $\angle $A = $\angle $P = $90^{\circ}$. If BC = 13 cm, PR = 5 cm, find AB.
Option 1: 12 cm
Option 2: 8 cm
Option 3: 10 cm
Option 4: 5 cm
Question : Select the correct statement about the properties of a triangle.
Option 1: The sum of two sides may be equal to the third side.
Option 2: The sum of two sides is always equal to the third side.
Option 3: The sum of two sides is always greater than the third side.
Option 4: The sum of two sides is always less than the third side.
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