Topic 10 - Congruent Triangles with Triangle Review

Front

What does AAA stand for in triangle congruence, and why is it not a valid reason to prove congruent triangles?

Back

AAA stands for Angle-Angle-Angle. It is not a valid reason to prove congruence because it only shows that triangles have the same shape, not necessarily the same size.

Front

What is the HL theorem in triangle congruence?

Back

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

Front

What is the Triangle Sum Theorem?

Back

The Triangle Sum Theorem states that the sum of the interior angles of a triangle is always 180 degrees.

Front

Can a triangle be formed with side lengths 10, 12, and 22? Explain why or why not.

Back

No, a triangle cannot be formed with these side lengths because they do not satisfy the triangle inequality theorem, which states that the sum of the lengths of any two sides must be greater than the length of the third side.

Front

What does SAS stand for in triangle congruence?

Back

SAS stands for Side-Angle-Side, which is 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 is the definition of congruent triangles?

Back

Congruent triangles are triangles that are identical in shape and size, meaning their corresponding sides and angles are equal.

Front

What is the difference between congruence and similarity in triangles?

Back

Congruence means that triangles are the same size and shape, while similarity means that triangles have the same shape but may be different sizes.

Front

What is the purpose of using triangle congruence postulates?

Back

Triangle congruence postulates are used to prove that two triangles are congruent, which helps in solving various geometric problems.

Front

List the main triangle congruence postulates and theorems.

Back

The main triangle congruence postulates and theorems are: SSS (Side-Side-Side), SAS (Side-Angle-Side), ASA (Angle-Side-Angle), AAS (Angle-Angle-Side), and HL (Hypotenuse-Leg for right triangles).

Front

How can you determine if two triangles are congruent using the SSS postulate?

Back

To determine if two triangles are congruent using the SSS postulate, you must show that all three sides of one triangle are equal to the three sides of the other triangle.