Question

hw 5: proving triangles congruent: sss & sas
state whether the triangles could be proven congruent, if possible, by sss or sas. then, write a congruency statement.
3.
the triangles ▼ congruent by ▼
△▼▼▼ ≅ △▼▼▼

Explanation:

Step1: Identify Given Information

We have two triangles, $\triangle TVS$ and $\triangle UVS$. From the diagram:

• $TV = VU$ (marked with tick marks, so these sides are congruent).
• $\angle TVS = \angle UVS$ (marked with the same angle symbol, so these angles are congruent).
• $VS$ is a common side to both triangles, so $VS = VS$ (reflexive property of congruence).

Step2: Determine Congruence Criterion

The SAS (Side - Angle - Side) congruence criterion states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.
Here, we have:

• Side $TV$ (of $\triangle TVS$) $\cong$ Side $VU$ (of $\triangle UVS$)
• Included angle $\angle TVS$ (of $\triangle TVS$) $\cong$ Included angle $\angle UVS$ (of $\triangle UVS$)
• Side $VS$ (common side) $\cong$ Side $VS$ (common side)

So, by SAS, the triangles are congruent.

Step3: Write Congruence Statement

Based on the correspondence of the congruent parts, the congruence statement is $\triangle TVS \cong \triangle UVS$.

Answer:

The triangles $\boldsymbol{\text{are}}$ congruent by $\boldsymbol{\text{SAS}}$.
$\boldsymbol{\triangle TVS \cong \triangle UVS}$