Triangle Congruence Worksheet With Answers - Practice Made Easy
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Triangle congruence is an essential concept in geometry that deals with determining when two triangles are congruent, meaning they are exactly the same size and shape. Understanding triangle congruence is vital for high school students, as it forms a fundamental part of both geometry and mathematical reasoning. In this article, we will discuss the different congruence criteria, provide practice problems, and include a worksheet with answers to help you grasp this essential topic effectively.
What is Triangle Congruence? 📐
Triangle congruence means that two triangles have the same size and shape, which can be proven using several criteria. When two triangles are congruent, their corresponding sides and angles are equal. The main congruence criteria for triangles are:
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Side-Side-Side (SSS): If all three sides of one triangle are equal to the three sides of another triangle, then the triangles are congruent.
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Side-Angle-Side (SAS): If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the triangles are congruent.
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Angle-Side-Angle (ASA): If two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the triangles are congruent.
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Angle-Angle-Side (AAS): 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 triangles are congruent.
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Hypotenuse-Leg (HL): This criterion is specific to right triangles. If the hypotenuse and one leg of a right triangle are equal to the hypotenuse and one leg of another right triangle, then the triangles are congruent.
Practice Problems 📝
Worksheet on Triangle Congruence
To help solidify your understanding of triangle congruence, here is a worksheet containing practice problems. The problems will utilize various congruence criteria, and your task will be to determine whether the given triangles are congruent or not.
Problems
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Triangle ABC and Triangle DEF
- AB = 5 cm, AC = 7 cm, BC = 8 cm
- DE = 5 cm, DF = 7 cm, EF = 8 cm
- Are the triangles congruent? (Use SSS)
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Triangle GHI and Triangle JKL
- GH = 6 cm, HI = 10 cm, ∠H = 50°
- JK = 6 cm, KL = 10 cm, ∠K = 50°
- Are the triangles congruent? (Use SAS)
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Triangle MNO and Triangle PQR
- ∠M = 30°, ∠N = 60°, MN = 10 cm
- ∠P = 30°, ∠Q = 60°, PQ = 10 cm
- Are the triangles congruent? (Use AAS)
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Triangle STU and Triangle VWX
- ST = 4 cm, ∠T = 70°, ∠U = 40°
- VW = 4 cm, ∠W = 70°, ∠X = 40°
- Are the triangles congruent? (Use ASA)
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Right Triangle YZA and Right Triangle BCD
- YZ = 5 cm, ZA = 12 cm (hypotenuse)
- BC = 5 cm, CD = 12 cm (hypotenuse)
- Are the triangles congruent? (Use HL)
Table of Answers
Here are the answers to the problems provided in the worksheet:
<table> <tr> <th>Problem</th> <th>Congruence Criteria Used</th> <th>Are They Congruent?</th> </tr> <tr> <td>1</td> <td>SSS</td> <td>Yes</td> </tr> <tr> <td>2</td> <td>SAS</td> <td>Yes</td> </tr> <tr> <td>3</td> <td>AAS</td> <td>Yes</td> </tr> <tr> <td>4</td> <td>ASA</td> <td>Yes</td> </tr> <tr> <td>5</td> <td>HL</td> <td>Yes</td> </tr> </table>
Important Notes About Triangle Congruence 🔍
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Always pay attention to the specific congruence criteria being used. Not all triangles can be proven congruent using any criteria.
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Keep in mind that the order of the sides and angles matters when labeling triangles. Corresponding angles and sides must match in pairs.
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It can be helpful to use diagrams or sketching out the triangles to visualize the congruence relationships better.
Conclusion
Triangle congruence is a vital concept in geometry that reinforces the understanding of relationships between shapes. Mastering the criteria for determining triangle congruence will not only help you in solving various geometric problems but also provide a solid foundation for advanced mathematical concepts. Practice using worksheets like the one provided, and remember to refer back to the congruence criteria to enhance your understanding. Happy studying! 📚✏️