Question

In Exercises 13 to $18,$ use only the given information to state the reason why $\triangle A B C \cong \triangle D B C .$ Redraw the figure and use marks like those used in Exercises 9 to 12 . $$\overline{A C}=\overline{C D}, \overline{A B} \equiv \overline{B D}, \text { and } \overline{C B}=\overline{C B} \text { (by Identity) }$$ (GRAPH CANT COPY)

Name: Problem 17, Chapter 3: Elementary Geometry for College Students
Uploaded: 2021-11-19T23:33:00-08:00
Duration: 18 s
Channel: James Kiss
Description: In Exercises 13 to 18, use only the given information to state the reason why A B C ≅D B C . Redraw the figure and use marks like those used in Exercises 9 to 12 . A C=C D, A B ≡B D, and C B=C B (by Identity) (GRAPH CANT COPY)

   In Exercises 13 to $18,$ use only the given information to state the reason why $\triangle A B C \cong \triangle D B C .$ Redraw the figure and use marks like those used in Exercises 9 to 12 .
$$\overline{A C}=\overline{C D}, \overline{A B} \equiv \overline{B D}, \text { and } \overline{C B}=\overline{C B} \text { (by Identity) }$$
(GRAPH CANT COPY)

Elementary Geometry for College Students

Daniel C. Alexander,… 6th Edition

Chapter 3, Problem 17

Instant Answer

Solved by Expert James Kiss

11/19/2021

Step 1

Step 1: First, we know that $\overline{A C}=\overline{C D}$, which means that side AC is congruent to side CD. Show more…

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In Exercises 13 to $18,$ use only the given information to state the reason why $\triangle A B C \cong \triangle D B C .$ Redraw the figure and use marks like those used in Exercises 9 to 12 . $$\overline{A C}=\overline{C D}, \overline{A B} \equiv \overline{B D}, \text { and } \overline{C B}=\overline{C B} \text { (by Identity) }$$ (GRAPH CANT COPY)

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Key Concepts

Triangle Congruence

Triangle congruence refers to the concept that two triangles are congruent if all of their corresponding sides and angles are equal. When triangles are congruent, every characteristic of one triangle matches the other, ensuring they are identical in shape and size.

SSS (Side-Side-Side) Postulate

The SSS postulate is a fundamental principle in geometry which states that if three pairs of corresponding sides of two triangles are congruent, then the triangles themselves are congruent. This postulate is applied in the problem by showing that each pair of corresponding sides in the two triangles is equal.

Reflexive Property

The reflexive property states that any geometric segment or angle is equal to itself. In the context of triangle congruence, it is used to establish that a side shared by both triangles is congruent to itself, providing one of the necessary conditions for applying the SSS postulate.

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