$CATEGORY: Maths - TicTacLearn/6. Triangles/6. Triangles--Criteria for Similarity of Triangles

//Multiple Choice

Which of the following is the correct definition of the SSS criterion for congruence? {
= Two triangles are congruent if three sides of one triangle are equal to the three corresponding sides of the other triangle.
~ Two triangles are congruent if one angle and the included side of one triangle are equal to the corresponding parts of the other triangle.
~ Two triangles are congruent if two sides and the included angle of one triangle are equal to the corresponding parts of the other triangle.
~ Two triangles are congruent if all their angles are equal.
}

In △ABC and △DEF, AB\= DE, BC \= EF, and AC \= DF. What can you conclude? {
= △ABC ≅ △DEF by SSS criterion.
~ △ABC ≅ △DEF by ASA criterion.
~ △ABC and △DEF are similar but not congruent.
~ No conclusion can be drawn.
}

If two triangles are congruent by the SSS criterion, then {
= Their areas are equal.
~ Their perimeters are different.
~ Their angles may not be equal.
~ Their corresponding sides are proportional.
}

Which of the following conditions does NOT satisfy the SSS criterion? {
~ AB \= PQ, BC \= QR, AC \= PR.
~ AB \= QR, BC \= PR, AC \= PQ.
~ AB \= PR, BC \= PQ, AC \= QR.
= AB \= PQ, BC \= PR, AC \= QR.
}

SSS Criterion ensures that {
= Both angles and sides are equal.
~ Only angles are equal.
~ Only sides are equal.
~ None of the above.
}

//True or False

The SSS criterion can be used even if only two sides of a triangle are known. {F}

Congruent triangles always have equal areas. {T}

If two triangles satisfy the SSS criterion, then their perimeters will be equal. {T}

The SSS criterion ensures that all angles in the two triangles are proportional. {F}

The SSS criterion is valid only for equilateral triangles. {F}

//Numericals



//Fill in the blanks

The SSS criterion states that if three sides of one triangle are ______ to the corresponding three sides of another triangle, then the triangles are congruent. {
~ proportional
= equal
~ larger
~ smaller
}

If △ABC and △PQR satisfy the SSS criterion, then their corresponding ______ will also be equal. {
~ sides
= angles
~ areas
~ perimeters
}

The SSS criterion proves that two triangles are ______ in shape and size. {
= identical
~ different
~ similar
~ proportional
}

The SSS criterion requires the comparison of ______ sides of two triangles. {
~ one
~ two
= three
~ no
}

If all sides of one triangle are equal to the corresponding sides of another triangle, then the two triangles are ______. {
~ similar
= congruent
~ isosceles
~ equilateral
}

The SSS criterion compares ______ of the triangles without considering their angles initially. {
= sides
~ vertices
~ altitudes
~ medians
}

If two triangles satisfy the SSS criterion, their ______ will always be equal. {
~ volumes
= perimeters
~ bases
~ heights
}

The property of congruence states that triangles with equal sides are ______ in all respects. {
~ different
= congruent
~ similar
~ proportional
}

If △PQR ≅ △XYZ by the SSS criterion, then side PQ corresponds to side ______. {
~ YZ
= XY
~ XZ
~ ZY
}

To prove the congruence of two triangles by the SSS criterion, all three sides must be ______ in length. {
~ proportional
= equal
~ parallel
~ unequal
}

//Match the following

Match the following items from Column A with their correct corresponding options from Column B\:
{
=SSS Criterion -> Based on SSS, SAS, ASA, and RHS criteria
=Congruent Triangles -> Have equal corresponding sides and angles
=Corresponding Sides -> Equal sides in the same relative position
=Area of Congruent Triangles -> Always equal
=Congruence Property -> Ensures all sides and angles are equal
}



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