Geometry - Review 4.1-4.5 Flashcard

Front

What does SAS stand for in triangle congruence?

Back

SAS stands for Side-Angle-Side, a theorem 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 AAS theorem in triangle congruence?

Back

AAS stands for Angle-Angle-Side, which states that 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

Define the HL theorem in triangle congruence.

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 equal to the hypotenuse and one leg of another right triangle, then the triangles are congruent.

Front

What is the difference between SSA and other triangle congruence theorems?

Back

SSA (Side-Side-Angle) does not guarantee triangle congruence, as it can lead to ambiguous cases where two different triangles can be formed.

Front

How do you solve for x in the equation 4x - 2 + 75 = 12x + 1?

Back

Combine like terms: 4x + 73 = 12x + 1. Then, isolate x: 73 - 1 = 12x - 4x, leading to 72 = 8x, so x = 9.

Front

What is the significance of triangle congruence theorems?

Back

Triangle congruence theorems are used to prove that two triangles are identical in shape and size, which is essential in various geometric proofs and applications.

Front

What does ASA stand for in triangle congruence?

Back

ASA stands for Angle-Side-Angle, which states that 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 is the relationship between congruent triangles and their corresponding parts?

Back

If two triangles are congruent, then their corresponding sides and angles are also congruent.

Front

How can you identify congruent triangles using the AAS theorem?

Back

To use the AAS theorem, you need to show that two angles and a non-included side of one triangle are equal to two angles and the corresponding non-included side of another triangle.

Front

What is the purpose of using triangle congruence theorems in geometry?

Back

Triangle congruence theorems help in establishing relationships between different geometric figures, proving properties, and solving problems involving triangles.