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AGHI is congruent to AJKL. (a) Identify the true statement. JK 쓸 GH JK 쓸 KL JK = JL JK 쓸 GI JK 스 HI (b) Identify the true statement. HI 쓴 JL HI 쓴 JK HI = GH HI 쓴 KL HI 쓴 GI (c) Identify the true statement. JL = GI JL 쓴 HI JL = JK O JL = KL O JL E GH

AGHI is congruent to AJKL. (a) Identify the true statement. JK 쓸 GH JK 쓸 KL JK = JL JK 쓸 GI JK 스 HI (b) Identify the true statement. HI 쓴 JL HI 쓴 JK HI = GH HI 쓴 KL HI 쓴 GI (c) Identify the true statement. JL = GI JL 쓴 HI JL = JK O JL = KL O JL E GH

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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### Congruent Triangles: Understanding Corresponding Parts In geometry, when we say two triangles are congruent, it means they have the exact same size and shape, and their corresponding sides and angles are equal. This is a fundamental concept in Euclidean geometry, often denoted using the symbol “≅”. #### Triangles Given: Let's consider two triangles, △GHI and △JKL, which are congruent to each other. --- #### (a) Identify the True Statement **Problem Statement:** Given the congruency of triangles △GHI and △JKL, identify the true statement among the following options regarding the corresponding sides: - ○ JK ≅ GH - ● JK ≅ KL - ○ JK ≅ JL - ○ JK ≅ GI - ○ JK ≅ HI **Explanation:** The correct pair of congruent sides between △GHI and △JKL should match the corresponding sides accurately. However, in this activity, the checked statement with `JK ≅ KL` is incorrect as per the congruency rules. --- #### (b) Identify the True Statement **Problem Statement:** Again, identify another true statement regarding the corresponding sides: - ● HI ≅ JL - ○ HI ≅ JK - ○ HI ≅ GH - ○ HI ≅ KL - ○ HI ≅ GI **Explanation:** In this case, the correct correspondence between the sides is given as HI ≅ JL, which aligns with the congruency of the triangles. Nevertheless, it is marked incorrect in the provided image. --- #### (c) Identify the True Statement **Problem Statement:** Lastly, find the true statement about the corresponding sides: - ○ JL ≅ GI - ● JL ≅ HI - ○ JL ≅ JK - ○ JL ≅ KL - ○ JL ≅ GH **Explanation:** Once more, the true corresponding sides must be accurately identified. The choice provided, JL ≅ HI, is indeed the correct correspondence according to congruency principles. However, it is marked incorrect in the provided image. --- ### Closing Notes Understanding congruent triangles helps in solving various geometric problems, ensuring that we correctly match each corresponding part—both angles and sides. This knowledge is critical not only in theoretical mathematics but also in practical applications such as engineering and physics.
Transcribed Image Text:### Congruent Triangles: Understanding Corresponding Parts In geometry, when we say two triangles are congruent, it means they have the exact same size and shape, and their corresponding sides and angles are equal. This is a fundamental concept in Euclidean geometry, often denoted using the symbol “≅”. #### Triangles Given: Let's consider two triangles, △GHI and △JKL, which are congruent to each other. --- #### (a) Identify the True Statement **Problem Statement:** Given the congruency of triangles △GHI and △JKL, identify the true statement among the following options regarding the corresponding sides: - ○ JK ≅ GH - ● JK ≅ KL - ○ JK ≅ JL - ○ JK ≅ GI - ○ JK ≅ HI **Explanation:** The correct pair of congruent sides between △GHI and △JKL should match the corresponding sides accurately. However, in this activity, the checked statement with `JK ≅ KL` is incorrect as per the congruency rules. --- #### (b) Identify the True Statement **Problem Statement:** Again, identify another true statement regarding the corresponding sides: - ● HI ≅ JL - ○ HI ≅ JK - ○ HI ≅ GH - ○ HI ≅ KL - ○ HI ≅ GI **Explanation:** In this case, the correct correspondence between the sides is given as HI ≅ JL, which aligns with the congruency of the triangles. Nevertheless, it is marked incorrect in the provided image. --- #### (c) Identify the True Statement **Problem Statement:** Lastly, find the true statement about the corresponding sides: - ○ JL ≅ GI - ● JL ≅ HI - ○ JL ≅ JK - ○ JL ≅ KL - ○ JL ≅ GH **Explanation:** Once more, the true corresponding sides must be accurately identified. The choice provided, JL ≅ HI, is indeed the correct correspondence according to congruency principles. However, it is marked incorrect in the provided image. --- ### Closing Notes Understanding congruent triangles helps in solving various geometric problems, ensuring that we correctly match each corresponding part—both angles and sides. This knowledge is critical not only in theoretical mathematics but also in practical applications such as engineering and physics.
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