Questions: Select ALL statements that are true about the triangles. (Do not add stuff to the diagram) a. ABC ≅ DCB because of Angle-Side-Angle (ASA) b. ABC ≅ DCB because of Angle-Angle-Angle (AAA) c. ABC ≅ DCB because of Side-Side-Side (SSS) d. ABC ≅ DCB because of Side-Angle-Side (SAS) e. ABC ≅ DCB because of Angle-Side-Side (ASS)

Select ALL statements that are true about the triangles. (Do not add stuff to the diagram) a. ABC ≅ DCB because of Angle-Side-Angle (ASA) b. ABC ≅ DCB because of Angle-Angle-Angle (AAA) c. ABC ≅ DCB because of Side-Side-Side (SSS) d. ABC ≅ DCB because of Side-Angle-Side (SAS) e. ABC ≅ DCB because of Angle-Side-Side (ASS)
Transcript text: Select ALL statements that are true about the triangles. (Do not add stuff to the diagram) a. $\mathrm{ABC} \cong \mathrm{DCB}$ because of Angle-Side-Angle (ASA) b. $A B C \cong D C B$ because of Angle-Angle-Angle (AAA) c. $\mathrm{ABC} \cong \mathrm{DCB}$ because of Side-Side-Side (SSS) d. $\mathrm{ABC} \cong \mathrm{DCB}$ because of Side-Angle-Side (SAS) e. $A B C \cong D C B$ because of Angle-Side-Side (ASS)
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Solution

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Solution Steps

Step 1: Analyze the given information

Triangle ABC has two angles marked congruent to two angles in triangle DCB. Side BC is shared by both triangles and therefore congruent to itself.

Step 2: Determine the congruent triangles

Since two angles and the included side are congruent, the triangles are congruent by the Angle-Side-Angle (ASA) postulate.

Final Answer

a. ABC ≅ DCB because of Angle-Side-Angle (ASA)

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