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

//Multiple Choice

The SAS criterion states that two triangles are similar if\: {
~ Two sides of one triangle are equal to two sides of the other triangle.
~ One angle of one triangle is equal to one angle of the other triangle.
= Two sides of one triangle are proportional to two sides of the other triangle, and the included angles are equal.
~ The corresponding angles of the two triangles are equal.
}

In △ABC and △PQR, if AB/PQ \= AC/PR and ∠A \= ∠P, then\: {
~ △ABC ≅ △PQR
= △ABC and △PQR are similar by SAS criterion.
~ △ABC and △PQR are not similar.
~ △ABC and △PQR are similar by AAA criterion.
}

Which of the following conditions is NOT required for the SAS similarity criterion? {
~ The corresponding sides are proportional.
~ The included angles are equal.
= All three pairs of angles are equal.
~ Two pairs of corresponding sides are proportional.
}

If two triangles are similar by the SAS criterion, then\: {
= Their areas are proportional to the square of the corresponding sides.
~ Their angles may not be equal.
~ Their perimeters are equal.
~ Their volumes are proportional.
}

In △DEF and △XYZ, DE/XY \= 3/5, EF/YZ \= 3/5, and ∠E \= ∠Y. Which criterion ensures their similarity? {
~ SSS Criterion
~ ASA Criterion
= SAS Criterion
~ None of the above
}

//True or False

The SAS criterion for similarity requires all three sides of both triangles to be proportional. {F}

If two triangles satisfy the SAS criterion, then their corresponding angles will also be equal. {T}

The SAS similarity criterion can be applied to any two polygons. {F}

If the SAS criterion is satisfied, then the two triangles have the same shape but may differ in size. {T}

The included angle in the SAS criterion must be proportional to ensure similarity. {F}

//Numericals



//Fill in the blanks

The SAS criterion for similarity requires two sides to be ______ and the included angle to be equal. {
~ equal
~ parallel
= proportional
~ perpendicular
}

For triangles to be similar by the SAS criterion, the included angle must be ______ for both triangles. {
= equal
~ proportional
~ smaller
~ larger
}

In △ABC and △PQR, if AB/PQ \= AC/PR and ∠A \= ______, the triangles are similar by SAS criterion. {
~ ∠Q
~ ∠R
= ∠P
~ ∠C
}

The SAS similarity criterion involves comparing ______ pairs of sides and one pair of included angles. {
~ one
= two
~ three
~ four
}

If the sides of one triangle are proportional to the corresponding sides of another triangle, and the included angles are equal, the triangles are ______. {
~ congruent
= similar
~ isosceles
~ equilateral
}

//Match the following

Match the following items from Column A with their correct corresponding options from Column B\:
{
=SAS Similarity Criterion -> Corresponding sides are proportional, and the included angle is equal.
=Included Angle -> The angle formed by two given sides of a triangle.
=Similar Triangles -> Triangles that have the same shape but not necessarily the same size.
=Proportional Sides -> The ratio of corresponding sides is the same.
=Angle Equality -> Equal angles ensure similarity in triangles.
}



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