Proving Triangle Congruence: SSS Theorem Insights

What does the SSS theorem state about two triangles with three pairs of congruent sides?

• The triangles are similar.

• The triangles have equal perimeters.

• The triangles are congruent.

• The triangles have equal areas.

If two triangles share a side, which property can be used to state that the shared side is congruent to itself?

• Substitution Property

• Symmetric Property

• Reflexive Property

• Transitive Property

What is the key requirement for using the HL theorem?

• The triangles must be equilateral.

• The triangles must be right triangles.

• The triangles must be isosceles.

• The triangles must have congruent angles.

In the HL theorem, which sides must be congruent for the triangles to be congruent?

• One hypotenuse and one leg

• Two angles

• Two hypotenuses

• Two legs

Why can't the HL theorem be used if only the legs of two right triangles are congruent?

• Because the hypotenuses must also be congruent.

• Because the triangles must be equilateral.

• Because the angles must be congruent.

• Because the triangles must be isosceles.

When dealing with overlapping triangles, which property is often used to identify shared sides or angles?

• Substitution Property

• Transitive Property

• Symmetric Property

• Reflexive Property

In a proof involving right triangles, what is the significance of identifying right angles?

• It helps in using the SAS theorem.

• It helps in using the ASA theorem.

• It helps in using the HL theorem.

• It helps in using the SSS theorem.

Which theorem can be used if two sides and the included angle of two triangles are congruent?

• SSS

• HL

• ASA

• SAS

What does the term 'included angle' refer to in the context of the SAS theorem?

• An angle that is not between the two sides.

• An angle that is between the two sides.

• An angle that is congruent to another angle.

• An angle that is supplementary to another angle.

Why is it important to draw overlapping triangles separately when proving congruency?

• To avoid confusion and clearly see the congruent parts.

• To make the proof longer.

• To make the proof more complex.

• To use more theorems.