Question

Triangles brm and yht are shown determine if the given information is sufficient to conclude that the triangles are congruent and so named the congruent theorem or postulate that shows congruence

Answer 1

If two triangles are congruent, you need sufficient information. The most common ways to prove congruence are through Side-Angle-Side (SAS) Congruence, Side-Side-Side (SSS) Congruence, Angle-Side-Angle (ASA) Congruence, Angle-Angle-Side (AAS) Congruence, and Hypotenuse-Leg (HL) Congruence for Right Triangles.

In order to determine if two triangles are congruent, you need sufficient information. The most common ways to prove congruence are through:

1. 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.
2. Side-Side-Side (SSS) Congruence: If all three sides of one triangle are congruent to the corresponding three sides 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 for Right Triangles: If the hypotenuse and one leg of one right triangle are congruent to the hypotenuse and corresponding leg of another right triangle, then the triangles are congruent.

Check the information given for the triangles and see if it satisfies one of these congruence criteria. If it does, you can conclude that the triangles are congruent. If not, more information may be needed.

Answer 2

Without specific information about the sides or angles of triangles BRM and YHT, we cannot determine if they are congruent. We would need to know measurements that correspond to the congruency theorems or postulates like SSS, SAS, ASA, AAS, or HL.

Step-by-step explanation:

To determine if triangles BRM and YHT are congruent, we need to examine the given information to see if it satisfies any of the congruency theorems or postulates. The congruence of triangles is typically evaluated using one of several methods: Side-Side-Side (SSS), Side-Angle-Side (SAS), Angle-Side-Angle (ASA), Angle-Angle-Side (AAS), or Hypotenuse-Leg (HL) for right triangles.

Unfortunately, based on the question, no specific information about the sides or angles of the triangles is provided. To give a definitive answer, we would need details such as the lengths of corresponding sides or measures of corresponding angles. Without this information, we cannot apply the congruency theorems or postulates to conclude that the triangles are congruent.

If such information were available, and it matched one of the above theorems or postulates, then we could state the specific theorem or postulate that validates the congruence. For example, if all three sides of triangle BRM were equal in length to all three sides of triangle YHT, we could use the SSS Postulate to declare the triangles congruent.