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


//Multiple Choice

The AAA criterion for similarity states that two triangles are similar if\: {
= All three pairs of corresponding angles are equal.
~ All three pairs of corresponding sides are equal.
~ Two sides are proportional, and the included angle is equal.
~ None of the above.
}

If two triangles are similar by the AAA criterion, then\: {
= The ratios of their corresponding sides are equal.
~ The areas of the triangles are equal.
~ The perimeters of the triangles are the same.
~ They must be congruent.
}

In △ABC and △PQR, ∠A \= ∠P, ∠B \= ∠Q, and ∠C \= ∠R. Then\: {
~ △ABC and △PQR are congruent.
= △ABC and △PQR are similar by AAA criterion.
~ △ABC and △PQR are isosceles triangles.
~ △ABC and △PQR are equilateral triangles.
}

If △DEF \∼ △XYZ by the AAA criterion, then the ratio of their corresponding sides will be\: {
~ Equal to 1.
~ Different for each pair of sides.
= Equal for all pairs of sides.
~ Cannot be determined.
}

For AAA similarity, the corresponding angles of two triangles must\: {
~ Be supplementary.
= Be equal in measure.
~ Add up to 90°.
~ Be proportional to their sides.
}

//True or False

The AAA criterion for similarity ensures that two triangles have the same area. {F}

The AAA criterion does not require the sides of two triangles to be proportional. {T}

If all three angles of two triangles are equal, their corresponding sides must also be equal. {F}

Two triangles similar to the AAA criterion have equal corresponding angles and proportional corresponding sides. {T}

The AAA criterion can be used to prove congruence between two triangles. {F}

//Numericals



//Fill in the blanks

Two triangles are similar by the AAA criterion if all three ______ are equal. {
~ Sides
~ Medians
= Angles
~ Heights
}

If △PQR \∼ △XYZ by the AAA criterion, then the ratios of their corresponding sides are always ______. {
= Equal
~ Unequal
~ Complementary
~ Greater than 1
}

The AAA similarity criterion ensures that two triangles have the same ______ but may differ in size. {
= shape
~ Area
~ Perimeter
~ Volume
}

In △ABC and △DEF, if ∠A \= ∠D, ∠B \= ∠E, and ∠C \= ∠F, then the triangles are ______ by the AAA criterion. {
~ Congruent
= Similar
~ Isosceles
~ Right-angled
}

By the AAA criterion, the ratios of the perimeters of similar triangles are ______ to the ratios of their corresponding sides. {
~ Proportional
= Equal
~ Unequal
~ Independent
}

//Match the following

Match the following items from Column A with their correct corresponding options from Column B\:
{
=AAA Criterion -> Corresponding angles of two triangles are equal.
=Similar Triangles -> Triangles with the same shape but different sizes.
=Proportional Sides -> Corresponding sides of two triangles have the same ratio.
=Corresponding Angles -> Angles that match between two triangles.
=Equal Ratios -> Relationship between sides in similar triangles.
}



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