practice work: unit 2
name:
period:
1.
here is a diagram.

select all statements that are true about the triangles.
a triangles abc and dcb are congruent by the angle - angle triangle congruence theorem.
b triangles abc and bcd are congruent by the angle - side - angle triangle congruence theorem.
c triangles abc and bcd are congruent by the side - side - side triangle congruence theorem.
d triangles abc and dcb are congruent by the side - angle - side triangle congruence theorem.
e triangles abc and dcb are congruent by the side - side - side triangle congruence theorem.
f there is not enough information to determine if the triangles are congruent.

Question

practice work: unit 2
name:
period:
1.
here is a diagram.

select all statements that are true about the triangles.
a triangles abc and dcb are congruent by the angle - angle triangle congruence theorem.
b triangles abc and bcd are congruent by the angle - side - angle triangle congruence theorem.
c triangles abc and bcd are congruent by the side - side - side triangle congruence theorem.
d triangles abc and dcb are congruent by the side - angle - side triangle congruence theorem.
e triangles abc and dcb are congruent by the side - side - side triangle congruence theorem.
f there is not enough information to determine if the triangles are congruent.

Accepted Answer

# Brief Explanations:
- **Option A**: Angle - Angle (AA) congruence requires two angles, but we have side - angle - side or side - side - side info here, so A is wrong.
- **Option B**: Triangles $ABC$ and $BCD$ – the sides and angles don't match for ASA here, and the triangles are $ABC$ and $DCB$ (not $BCD$) for congruence, so B is wrong.
- **Option C**: Triangles $ABC$ and $BCD$ – incorrect triangle labels, and SSS would need three sides, but the correct triangles are $ABC$ and $DCB$. For $ABC$ and $DCB$, $AB\cong DC$, $AC\cong DB$, and $BC$ is common (so $BC\cong BC$), so SSS applies to $ABC$ and $DCB$, but option C labels the triangles as $ABC$ and $BCD$ (wrong), so C is wrong. Wait, no, let's re - check: Given $AB\cong DC$, $AC\cong DB$, and $BC$ is a common side. So for $\triangle ABC$ and $\triangle DCB$: $AB = DC$, $AC=DB$, $BC = BC$ (SSS). Also, we have $\angle A\cong\angle D$, $AB\cong DC$, $AC\cong DB$ (SAS).
- **Option D**: For $\triangle ABC$ and $\triangle DCB$, $AB\cong DC$ (side), $\angle A\cong\angle D$ (angle), $AC\cong DB$ (side) – this is SAS (Side - Angle - Side) congruence. So D is correct.
- **Option E**: For $\triangle ABC$ and $\triangle DCB$, $AB\cong DC$, $AC\cong DB$, and $BC$ is common (so $BC\cong BC$) – three sides, so SSS congruence. So E is correct.
- **Option F**: We have enough information (sides and angle congruence) to determine congruence, so F is wrong.

# Answer:
D. Triangles $ABC$ and $DCB$ are congruent by the Side - Angle - Side Triangle Congruence Theorem.
E. Triangles $ABC$ and $DCB$ are congruent by the Side - Side - Side Triangle Congruence Theorem.

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