Triangle Congruence

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 congruent to two angles and the corresponding non-included side of another triangle, then the triangles are congruent.

Front

What is the SAS postulate?

Back

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

Front

What does SSS stand for in triangle congruence?

Back

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

Front

What is the HL theorem?

Back

HL stands for Hypotenuse-Leg, a theorem applicable to right triangles that states if the hypotenuse and one leg of one right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent.

Front

What is the SSA condition?

Back

SSA stands for Side-Side-Angle, which is not a valid congruence condition for triangles, as it does not guarantee that the triangles are congruent.

Front

How can you prove triangles are congruent using AAS?

Back

To prove triangles are congruent using AAS, show that two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle.

Front

What is the difference between AAS and ASA?

Back

AAS (Angle-Angle-Side) involves two angles and a non-included side, while ASA (Angle-Side-Angle) involves two angles and the included side.

Front

When can you use the SSS postulate?

Back

You can use the SSS postulate when you know the lengths of all three sides of two triangles and can show they are equal.

Front

What is the significance of the included angle in SAS?

Back

In SAS, the included angle is the angle formed between the two sides being compared, and it is crucial for establishing congruence.

Front

Can you prove triangles are congruent with only two sides?

Back

No, you cannot prove triangles are congruent with only two sides unless you also have the included angle (SAS) or the third side (SSS).