Gr.9 Similar And Congruent Triangles

1) Decide whether the given triangles are congruent or not. Select the correct reason.

∆ABC ≡ ∆XYZ (∠S∠)

∆ABC ≡ ∆XYZ (S∠S)

∆ABC ≡ ∆XYZ (∠∠S)

Not Congruent

The correct reason is "SAS (Side-Angle-Side) Congruence". This means that two triangles are congruent if they have two sides and the included angle of one triangle equal to the corresponding sides and included angle of the other triangle. In this case, ∆ABC and ∆XYZ are congruent because they have the same side lengths and the same angle measures.

Explanation

The correct reason is "SAS (Side-Angle-Side) Congruence". This means that two triangles are congruent if they have two sides and the included angle of one triangle equal to the corresponding sides and included angle of the other triangle. In this case, ∆ABC and ∆XYZ are congruent because they have the same side lengths and the same angle measures.

2) Are the following triangle similar? Select the correct answer.

No, they're not similar.

Yes they are similar (S,S,S).

Yes they are similar (S,∠,S) .

Cannot be determined.

The correct answer is "Yes, they are similar (S,S,S)." This means that the triangles have three pairs of corresponding sides that are proportional in length. In other words, the ratios of the lengths of the corresponding sides of the triangles are equal. This is a property of similar triangles.

Explanation

The correct answer is "Yes, they are similar (S,S,S)." This means that the triangles have three pairs of corresponding sides that are proportional in length. In other words, the ratios of the lengths of the corresponding sides of the triangles are equal. This is a property of similar triangles.

3) Two triangles are similar if: Select ALL the relevant answers.

All the corresponding angles are equal

All the corresponding sides are proportional

Two equal sides and no equal corresponding angles

None of the above.

Two triangles are similar if all the corresponding angles are equal and all the corresponding sides are proportional. This means that the angles in both triangles are the same and the lengths of the corresponding sides are in the same ratio. If only two sides of the triangles are equal but the corresponding angles are not equal, or if the angles are equal but the corresponding sides are not proportional, then the triangles are not similar.

Explanation

Two triangles are similar if all the corresponding angles are equal and all the corresponding sides are proportional. This means that the angles in both triangles are the same and the lengths of the corresponding sides are in the same ratio. If only two sides of the triangles are equal but the corresponding angles are not equal, or if the angles are equal but the corresponding sides are not proportional, then the triangles are not similar.

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4) Using the given information in each pair of triangles, decide whether there is sufficient information to state that the triangles are congruent. If they are, select the correct reason.

∆ABC ≡ ∆DEF (∠∠S )

∆ABC ≡∆DEF (∠ S S )

Not congruent

∆ABC ≡∆DEF (∠ S∠ )

The correct reason for stating that ∆ABC is congruent to ∆DEF is because they have corresponding angles that are congruent. The notation (∠∠S) indicates that both pairs of corresponding angles are congruent. Therefore, the triangles are congruent.

Explanation

The correct reason for stating that ∆ABC is congruent to ∆DEF is because they have corresponding angles that are congruent. The notation (∠∠S) indicates that both pairs of corresponding angles are congruent. Therefore, the triangles are congruent.

5) Triangles are similar if: Select ALL the relevant answers.

All three pairs of corresponding sides are in the same proportion.

Two pairs of sides in the same proportion and the included angle equal.

They have the same shape, but cannot be different sizes.

All three pairs of corresponding angles are the same.

Triangles are similar if all three pairs of corresponding sides are in the same proportion, two pairs of sides are in the same proportion and the included angle is equal, and all three pairs of corresponding angles are the same. This means that the triangles have the same shape, but they may be different sizes.

Explanation

Triangles are similar if all three pairs of corresponding sides are in the same proportion, two pairs of sides are in the same proportion and the included angle is equal, and all three pairs of corresponding angles are the same. This means that the triangles have the same shape, but they may be different sizes.

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