Proving congruent triangles - REVIEW

Front

What does ASA stand for in triangle congruence?

Back

ASA stands for Angle-Side-Angle, a criterion for triangle congruence where two angles and the included side of one triangle are equal to two angles and the included side of another triangle.

Front

What does HL stand for in triangle congruence?

Back

HL stands for Hypotenuse-Leg, a criterion for triangle congruence that applies to right triangles, stating that 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 are the four main triangle congruence theorems?

Back

The four main triangle congruence theorems are: 1) SSS (Side-Side-Side), 2) SAS (Side-Angle-Side), 3) ASA (Angle-Side-Angle), and 4) AAS (Angle-Angle-Side).

Front

How can you prove two triangles are congruent using the SSS theorem?

Back

To prove two triangles are congruent using the SSS theorem, you must show that all three sides of one triangle are equal to the corresponding three sides of the other triangle.

Front

What is the difference between ASA and AAS in triangle congruence?

Back

ASA (Angle-Side-Angle) requires the included side between two angles to be equal, while AAS (Angle-Angle-Side) requires two angles and a non-included side to be equal.

Front

What is the significance of the included side in the ASA theorem?

Back

In the ASA theorem, the included side is crucial because it connects the two angles, ensuring that the triangles are congruent based on the specific arrangement of the angles and the side.

Front

Can two triangles be congruent if only one angle and two sides are known?

Back

No, two triangles cannot be proven congruent with only one angle and two sides unless the angle is included between the two sides (ASA) or the two sides are equal to the corresponding sides of another triangle (SAS).

Front

What is the criteria for using the HL theorem?

Back

The HL theorem can only be used for right triangles, where you need to show that the hypotenuse and one leg of one right triangle are equal to the hypotenuse and one leg of another right triangle.

Front

What is the importance of congruence in geometry?

Back

Congruence in geometry is important because it allows us to determine that two shapes are identical in size and shape, which is essential for solving problems related to measurements, constructions, and proofs.

Front

How do you identify congruent triangles in a diagram?

Back

To identify congruent triangles in a diagram, look for markings such as tick marks on sides or angle arcs that indicate equal lengths or angles, and apply the appropriate congruence theorems.