Triangle Congruence Worksheet: Questions & Answers Inside!
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Understanding triangle congruence is fundamental in geometry, and it has a wide variety of applications in mathematics and real-world problem solving. This blog post will explore key concepts related to triangle congruence, share a worksheet with questions, and provide answers to help you grasp these concepts effectively. Let’s dive in!
What is Triangle Congruence? 🤔
Triangle congruence refers to the idea that two triangles are congruent if they have the same size and shape. This can be established through several postulates and theorems, such as:
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Side-Side-Side (SSS) Postulate: 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) Postulate: 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) Postulate: 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) Theorem: If two angles and a non-included side of one triangle are equal to two angles and the corresponding non-included side of another triangle, then the triangles are congruent.
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Hypotenuse-Leg (HL) Theorem: In right triangles, if the hypotenuse and one leg of one triangle are equal to the hypotenuse and one leg of another triangle, then the triangles are congruent.
Triangle Congruence Worksheet 📝
Here’s a worksheet with some practical questions for practicing triangle congruence. Try to solve them before checking the answers provided below!
Questions
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Given triangle ABC, if AB = 5 cm, AC = 7 cm, and BC = 5 cm, use the SSS postulate to determine if triangle ABC is congruent to triangle DEF where DE = 5 cm, DF = 7 cm, and EF = 5 cm.
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If angle A = 45°, angle B = 60°, and side AB = 6 cm in triangle ABC, and angle D = 60°, angle E = 45°, and side DE = 6 cm in triangle DEF, are the triangles congruent? Use the AAS theorem.
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Triangle GHI has sides GH = 8 cm, HI = 10 cm, and GI = 6 cm. Triangle JKL has sides JK = 10 cm, KL = 6 cm, and JL = 8 cm. Use the SSS postulate to check for congruence.
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If angle X = 30°, side XY = 12 cm, and angle YZ = 30° in triangle XYZ, and angle A = 30°, side AB = 12 cm, and angle BA = 30° in triangle ABC, prove the triangles are congruent using the ASA postulate.
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In right triangles RST and UVW, if the hypotenuse RS = 10 cm, leg ST = 8 cm and hypotenuse UV = 10 cm, leg VW = 8 cm, can you conclude that the triangles are congruent using the HL theorem?
Answers
Now let’s check the answers to the questions above!
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Answer: Yes, triangle ABC is congruent to triangle DEF by the SSS postulate because all corresponding sides are equal: AB = DE, AC = DF, BC = EF.
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Answer: Yes, the triangles are congruent by the AAS theorem because two angles and the corresponding side are equal: Angle A = Angle E, Angle B = Angle D, and AB = DE.
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Answer: Yes, triangle GHI is congruent to triangle JKL by the SSS postulate as all the sides of triangle GHI are equal to the corresponding sides of triangle JKL.
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Answer: Yes, triangles XYZ and ABC are congruent by the ASA postulate as Angle X = Angle A, side XY = side AB, and Angle YZ = Angle BA.
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Answer: Yes, triangles RST and UVW are congruent by the HL theorem because the hypotenuses and one leg of both right triangles are equal.
Importance of Triangle Congruence in Real Life 🌍
Understanding triangle congruence not only helps in geometry problems but is also crucial in various real-life applications, such as:
- Architecture: Ensuring structural integrity by using congruent triangles in designs.
- Engineering: Designing components that must fit perfectly together.
- Computer Graphics: Creating realistic models and animations by manipulating triangular meshes.
Conclusion
Triangle congruence plays a vital role in understanding the properties and relationships of triangles, paving the way for more complex geometric concepts. By practicing with worksheets like the one provided above, you can reinforce your understanding and become more proficient in this essential area of mathematics. Remember, as you practice, you not only improve your skills in geometry but also enhance your logical thinking and problem-solving abilities. Happy learning! 📚✨