Unit 5: Congruent Triangles

Front

What does SSS stand for in triangle congruence?

Back

SSS stands for Side-Side-Side, a postulate that states if three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent.

Front

What does SAS stand for in triangle congruence?

Back

SAS stands for Side-Angle-Side, a postulate that states if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the triangles are congruent.

Front

What does ASA stand for in triangle congruence?

Back

ASA stands for Angle-Side-Angle, a postulate that states if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the triangles are congruent.

Front

What does AAS stand for in triangle congruence?

Back

AAS stands for Angle-Angle-Side, a theorem that states if two angles and a non-included side of one triangle are equal to two angles and the corresponding non-included side of another triangle, then the triangles are congruent.

Front

What is the significance of congruent triangles in geometry?

Back

Congruent triangles have the same size and shape, which means their corresponding sides and angles are equal. This property is fundamental in proving various geometric theorems.

Front

If ∆ABC ≅ ∆DEF, what can be inferred about their corresponding angles and sides?

Back

If ∆ABC ≅ ∆DEF, then ∠A ≅ ∠D, ∠B ≅ ∠E, ∠C ≅ ∠F and AB ≅ DE, BC ≅ EF, AC ≅ DF.

Front

Can triangles be congruent if they only have their angles equal?

Back

No, triangles cannot be congruent solely based on having equal angles (AAA). This is because AAA does not guarantee that the triangles are of the same size.

Front

What is the relationship between congruence and similarity in triangles?

Back

Congruent triangles are similar, but similar triangles are not necessarily congruent. Congruent triangles have equal corresponding sides and angles, while similar triangles have proportional sides and equal corresponding angles.

Front

How can you prove that two triangles are congruent using the SAS postulate?

Back

To prove two triangles are congruent using SAS, show that two sides of one triangle are equal to two sides of another triangle, and the angle between those sides is equal.

Front

What is the difference between congruence and equality in geometry?

Back

Congruence refers to figures that have the same shape and size, while equality refers to the numerical value of lengths or measures.