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Question 13:
Answer:
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Question 14:
.
Answer:
No, its not necessary. If the corresponding angles of two triangles are equal, then they may or may not be congruent.
They may have proportional sides as shown in the following figure:
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Question 15:
No, its not necessary. If the corresponding angles of two triangles are equal, then they may or may not be congruent.
They may have proportional sides as shown in the following figure:
Answer:
No, two triangles are not congruent if their two corresponding sides and one angle are equal. They will be congruent only if the said angle is the included angle between the sides.
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Question 16:
No, two triangles are not congruent if their two corresponding sides and one angle are equal. They will be congruent only if the said angle is the included angle between the sides.
Answer:
Both triangles have equal area due to the the same product of height and base. But they are not congruent.
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Question 17:
Both triangles have equal area due to the the same product of height and base. But they are not congruent.
Answer:
(i) the same length
(ii) the same measure
(iii)the same side length
(iv) the same radius
(v) the same length and the same breadth
(vi) equal parts
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Question 18:
(i) the same length
(ii) the same measure
(iii)the same side length
(iv) the same radius
(v) the same length and the same breadth
(vi) equal parts
Answer:
(i) False
This is because they can be equal only if they have equal sides.
(ii) True
This is because if squares have equal areas, then their sides must be of equal length.
(iii) False
For example, if a triangle and a square have equal area, they cannot be congruent.
(iv) False
For example, an isosceles triangle and an equilateral triangle having equal area cannot be congruent.
(v) False
They can be congruent if two sides and the included angle of a triangle are equal to the corresponding two sides and the included corresponding angle of another triangle.
(vi) True
This is because of the AAS criterion of congruency.
(vii) False
Their sides are not necessarily equal.
(viii) True
This is because of the AAS criterion of congruency.
(ix) False
This is because two right triangles are congruent if the hypotenuse and one side of the first triangle are respectively equal to the hypotenuse and the corresponding side of the second triangle.
(x) True
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