Triangle Congruence Worksheet with Answers and Solutions
Triangle congruence is a fundamental concept in geometry, and it’s essential to understand the different types of triangle congruence and how to prove them. In this worksheet, we’ll provide you with a comprehensive guide on triangle congruence, including examples, solutions, and answers.
What is Triangle Congruence?
Triangle congruence occurs when two triangles have the same size and shape. This means that corresponding angles and sides of the two triangles are equal. There are several types of triangle congruence, including:
- Side-Side-Side (SSS) Congruence: When three sides of one triangle are equal to the corresponding sides of another triangle.
- Side-Angle-Side (SAS) Congruence: When two sides and the included angle of one triangle are equal to the corresponding sides and angle of another triangle.
- Angle-Side-Angle (ASA) Congruence: When two angles and the included side of one triangle are equal to the corresponding angles and side of another triangle.
- Angle-Angle-Side (AAS) Congruence: When two angles and a non-included side of one triangle are equal to the corresponding angles and side of another triangle.
Examples and Solutions
Let’s work through some examples to illustrate the different types of triangle congruence.
Example 1: SSS Congruence
In the diagram below, we have two triangles, ABC and DEF.
| Triangle ABC | Triangle DEF |
|---|---|
| AB = 5 cm | DE = 5 cm |
| BC = 6 cm | EF = 6 cm |
| AC = 7 cm | DF = 7 cm |
Solution: Since the three sides of triangle ABC are equal to the corresponding sides of triangle DEF, we can conclude that triangle ABC is congruent to triangle DEF by SSS congruence.
Example 2: SAS Congruence
In the diagram below, we have two triangles, GHI and JKL.
| Triangle GHI | Triangle JKL |
|---|---|
| GH = 8 cm | JK = 8 cm |
| HI = 9 cm | KL = 9 cm |
Solution: Since two sides and the included angle of triangle GHI are equal to the corresponding sides and angle of triangle JKL, we can conclude that triangle GHI is congruent to triangle JKL by SAS congruence.
Example 3: ASA Congruence
In the diagram below, we have two triangles, MNO and PQR.
| Triangle MNO | Triangle PQR |
|---|---|
Solution: Since two angles and the included side of triangle MNO are equal to the corresponding angles and side of triangle PQR, we can conclude that triangle MNO is congruent to triangle PQR by ASA congruence.
Notes:
- Triangle congruence can be proven using various methods, including SSS, SAS, ASA, and AAS congruence.
- When proving triangle congruence, it’s essential to ensure that the corresponding parts of the two triangles are equal.
- Triangle congruence is a fundamental concept in geometry, and it’s used to solve problems in various areas, including trigonometry, graph theory, and engineering.
Now, let’s summarize the key points:
Triangle congruence occurs when two triangles have the same size and shape. There are several types of triangle congruence, including SSS, SAS, ASA, and AAS congruence. Each type of triangle congruence has its own set of conditions that must be met. We can use various methods to prove triangle congruence, including SSS, SAS, ASA, and AAS congruence.
What is the difference between SSS and SAS congruence?
+SSS congruence occurs when three sides of one triangle are equal to the corresponding sides of another triangle, while SAS congruence occurs when two sides and the included angle of one triangle are equal to the corresponding sides and angle of another triangle.
Can you prove triangle congruence using only two sides?
+No, you cannot prove triangle congruence using only two sides. You need to have at least two sides and an angle, or three sides, to prove triangle congruence.
What is the importance of triangle congruence in real-life applications?
+Triangle congruence has numerous applications in various fields, including engineering, architecture, physics, and computer science. It’s used to design and build structures, model real-world phenomena, and solve complex problems.
Related Terms:
- Triangle congruence Proofs Worksheet
- Triangle Congruence Worksheet PDF
- Triangle Congruence Worksheet #1
