In Exercises 33 to 36, the methods to be used are 5 ss, SAS. ASA, and AAS. Given that R S T ≅R V

Name: Problem 33, Chapter 3: Elementary Geometry for College Students
Uploaded: 2021-11-20T17:02:08-08:00
Duration: 1 min 11 s
Channel: James Kiss
Description: In Exercises 33 to 36, the methods to be used are 5 ss, SAS. ASA, and AAS. Given that R S T ≅R V U, does it follow that R S U is also congruent to R V T ? Name the method, if any, used in arriving at this conclusion. (GRAPH CANT COPY)

step 1 The question is if we knew that triangles RST and RVU were already congruent, would it follow th

Question

In Exercises 33 to $36,$ the methods to be used are $5 \mathrm{ss}$, SAS. ASA, and AAS. Given that $\triangle R S T \cong \triangle R V U,$ does it follow that $\triangle R S U$ is also congruent to $\triangle R V T$ ? Name the method, if any, used in arriving at this conclusion. (GRAPH CANT COPY)

   In Exercises 33 to $36,$ the methods to be used are $5 \mathrm{ss}$, SAS. ASA, and AAS.
Given that $\triangle R S T \cong \triangle R V U,$ does it follow that $\triangle R S U$ is also congruent to $\triangle R V T$ ? Name the method, if any, used in arriving at this conclusion.
(GRAPH CANT COPY)

Elementary Geometry for College Students

Daniel C. Alexander,… 6th Edition

Chapter 3, Problem 33

Instant Answer

Solved by Expert James Kiss

11/20/2021

Step 1

This means that the corresponding sides and angles of these two triangles are equal. Show more…

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In Exercises 33 to $36,$ the methods to be used are $5 \mathrm{ss}$, SAS. ASA, and AAS. Given that $\triangle R S T \cong \triangle R V U,$ does it follow that $\triangle R S U$ is also congruent to $\triangle R V T$ ? Name the method, if any, used in arriving at this conclusion. (GRAPH CANT COPY)

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Key Concepts

Triangle Congruence Criteria

This concept refers to the conditions under which two triangles can be declared congruent. Common criteria include side?side?side (SSS), side?angle?side (SAS), angle?side?angle (ASA), and angle?angle?side (AAS). These criteria allow one to determine that two triangles are identical in shape and size by comparing their corresponding sides and angles. The problem involves using one of these methods to relate different triangles by a reordering of vertices based on the known congruence.

Corresponding Parts of Congruent Triangles (CPCTC)

Once two triangles are proven congruent using any of the congruence criteria, we know that all corresponding sides and angles are equal. This principle, often referred to as CPCTC, is used to justify that additional triangles (formed by a reordering of vertices, for example) are also congruent, since the equality of their corresponding parts follows directly from the original congruence.

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