Which congruence criteria can be used to prove the triangles are congruent?
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There are several congruence criteria that can be used to prove triangles are congruent. Here are the most commonly used ones:
1. Side-Side-Side (SSS) congruence: If the three sides of one triangle are congruent to the corresponding three sides of another triangle, then the triangles are congruent.
2. Side-Angle-Side (SAS) congruence: 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.
3. Angle-Side-Angle (ASA) congruence: If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.
4. Angle-Angle-Side (AAS) congruence: 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.
5. Hypotenuse-Leg (HL) congruence: If the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent.
Remember to apply these criteria based on the given information and use them in the correct sequence to establish congruence between the triangles.
There are several congruence criteria that can be used to prove that two triangles are congruent. These criteria are often referred to as postulates or theorems. The most commonly used congruence criteria are:
1. Side-Side-Side (SSS) Criterion: This criterion states that if the three sides of one triangle are congruent to the corresponding three sides of another triangle, then the two triangles are congruent.
2. Side-Angle-Side (SAS) Criterion: This criterion states that if two sides and the included angle of one triangle are congruent to the corresponding two sides and included angle of another triangle, then the two triangles are congruent.
3. Angle-Side-Angle (ASA) Criterion: This criterion states that if two angles and the included side of one triangle are congruent to the corresponding two angles and included side of another triangle, then the two triangles are congruent.
4. Angle-Angle-Side (AAS) Criterion: This criterion states that if two angles and a non-included side of one triangle are congruent to the corresponding two angles and non-included side of another triangle, then the two triangles are congruent.
5. Hypotenuse-Leg (HL) Criterion (for right triangles only): This criterion states that if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the two triangles are congruent.
To use these congruence criteria, you need to compare the corresponding sides and angles of two triangles and determine if they are congruent. If all the required parts match up, you can conclude that the triangles are congruent based on the applicable congruence criterion.