Congruent Triangles Geometry Worksheet Answers

Congruent Triangles Geometry Worksheet Answers

In geometry, congruent triangles are triangles that have the same size and shape. This means that their corresponding angles and sides are equal. In this article, we will explore the concept of congruent triangles and provide answers to a geometry worksheet on the topic.

What are Congruent Triangles?

Congruent triangles are triangles that have the same size and shape. This means that their corresponding angles and sides are equal. In other words, if two triangles are congruent, then their corresponding parts (angles and sides) are also congruent.

Criteria for Congruent Triangles

There are several criteria that can be used to determine if two triangles are congruent. These include:

• Side-Side-Side (SSS) Congruence: If three sides of one triangle are equal to three sides of another triangle, then the two triangles are congruent.
• Side-Angle-Side (SAS) Congruence: If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the two triangles are congruent.
• Angle-Side-Angle (ASA) Congruence: If two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the two triangles are congruent.
• Angle-Angle-Side (AAS) Congruence: If two angles and a non-included side of one triangle are equal to two angles and a non-included side of another triangle, then the two triangles are congruent.

Worksheet Answers

Here are the answers to a geometry worksheet on congruent triangles:

1. Determine if the following triangles are congruent. If so, state the congruence criterion.

Triangle A: ∆ABC with sides AB = 5, BC = 6, AC = 7 Triangle B: ∆DEF with sides DE = 5, EF = 6, DF = 7

Answer: Yes, the triangles are congruent by SSS congruence.

2. Determine if the following triangles are congruent. If so, state the congruence criterion.

Triangle A: ∆GHI with sides GH = 8, HI = 9, GI = 10 and angle G = 45° Triangle B: ∆JKL with sides JK = 8, KL = 9, JL = 10 and angle J = 45°

Answer: Yes, the triangles are congruent by SAS congruence.

3. Determine if the following triangles are congruent. If so, state the congruence criterion.

Triangle A: ∆MNO with sides MN = 11, NO = 12, MO = 13 and angles M = 60°, N = 80° Triangle B: ∆PQR with sides PQ = 11, QR = 12, PR = 13 and angles P = 60°, Q = 80°

Answer: Yes, the triangles are congruent by ASA congruence.

4. Determine if the following triangles are congruent. If so, state the congruence criterion.

Triangle A: ∆STU with sides ST = 14, TU = 15, SU = 16 and angles S = 30°, T = 60° Triangle B: ∆VWX with sides VW = 14, WX = 15, VX = 16 and angles V = 30°, W = 60°

Answer: Yes, the triangles are congruent by AAS congruence.

📝 Note: The answers to these questions assume that the triangles are correctly labeled and that the given information is accurate.

Real-World Applications of Congruent Triangles

Congruent triangles have many real-world applications, including:

• Architecture: Congruent triangles are used in the design of buildings, bridges, and other structures to ensure that they are symmetrical and stable.
• Engineering: Congruent triangles are used in the design of machines, mechanisms, and other devices to ensure that they are efficient and effective.
• Art: Congruent triangles are used in the creation of art, including paintings, sculptures, and other forms of visual art.

Conclusion

In conclusion, congruent triangles are an important concept in geometry that have many real-world applications. By understanding the criteria for congruent triangles, including SSS, SAS, ASA, and AAS congruence, we can determine if two triangles are congruent and apply this knowledge to solve problems in a variety of fields.