Congruent triangles are two or more triangles with the same size and shape. They have exactly the same angles and the same lengths of the corresponding sides. Congruent triangles can be identified and compared by the use of a special theorem called the Side-Side-Side (SSS) Theorem, or the Side-Angle-Side (SAS) Theorem. These theorems are commonly used to solve problems related to congruent triangles.
Quiz 4-2: Congruent Triangles SSS and SAS
Quiz 4-2 is a quiz that tests your knowledge of the SSS and SAS theorems for congruent triangles. It requires you to identify two or more congruent triangles and determine the types of congruency based on the theorems. The quiz consists of several questions that require you to identify congruent triangles and determine the types of congruency.
How to Solve Quiz 4-2: Congruent Triangles SSS and SAS
To solve this quiz, you must first identify the congruent triangles by comparing their sides and angles. If the sides and angles of two triangles are equal, then they are congruent. After identifying the congruent triangles, you must determine the type of congruency by using the SSS or SAS theorem. If the triangles have three sides with equal lengths, then the congruency is SSS. If two sides and the included angle are equal, then the congruency is SAS.
Examples of Quiz 4-2: Congruent Triangles SSS and SAS
Example 1: Determine if the triangles ABC and XYZ are congruent and identify the type of congruency. Triangle ABC has sides AB = 5, BC = 6, CA = 7 and angles A = 50°, B = 70°, C = 60°. Triangle XYZ has sides XY = 5, YZ = 6, XZ = 7 and angles X = 50°, Y = 70°, Z = 60°. The two triangles are congruent by the SSS theorem, since all three sides have equal lengths.
Example 2: Determine if the triangles ABC and XYZ are congruent and identify the type of congruency. Triangle ABC has sides AB = 5, BC = 8, CA = 7 and angles A = 45°, B = 90°, C = 45°. Triangle XYZ has sides XY = 5, YZ = 8, XZ = 7 and angles X = 45°, Y = 90°, Z = 45°. The two triangles are congruent by the SAS theorem, since two sides and the included angle are equal.
In conclusion, Quiz 4-2 is an excellent way to test your knowledge of the SSS and SAS theorems for congruent triangles. To solve this quiz, you must first identify the congruent triangles by comparing their sides and angles. You must then determine the type of congruency by using the SSS or SAS theorem. Examples of the quiz are provided to help you understand how the theorems are used to find congruent triangles.
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