Question

question 21 of 25

what else would need to be congruent to show that \\(\delta stu \cong \delta jkl\\) by sas?

given:
\\(\overline{st} \cong \overline{jk}\\)
\\(\angle s \cong \angle j\\)

a. \\(\overline{tu} \cong \overline{jl}\\)
b. \\(\overline{su} \cong \overline{kl}\\)
c. \\(\overline{su} \cong \overline{jl}\\)
d. \\(\overline{tu} \cong \overline{kl}\\)

Explanation:

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<reasoning>

Identify the given congruent parts

Using the Triangle Congruence Postulates knowledge point
Given:
\[

$$\begin{aligned} &\overline{ST} \cong \overline{JK} \quad (\text{Side})\\ &\angle S \cong \angle J \quad (\text{Angle}) \end{aligned}$$

\]

Determine the required side for SAS

Using the Triangle Congruence Postulates knowledge point
\[

$$\begin{aligned} &\text{SAS requires the angle to be included between the two sides.}\\ &\text{For }\Delta STU\text{, }\angle S\text{ is included between }\overline{ST}\text{ and }\overline{SU}.\\ &\text{For }\Delta JKL\text{, }\angle J\text{ is included between }\overline{JK}\text{ and }\overline{JL}.\\ &\text{Therefore, we need: }\overline{SU} \cong \overline{JL} \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>A. \(\overline{TU} \cong \overline{JL}\)</mcq-option>
<mcq-option>B. \(\overline{SU} \cong \overline{KL}\)</mcq-option>
<mcq-correct>C. \(\overline{SU} \cong \overline{JL}\)</mcq-correct>
<mcq-option>D. \(\overline{TU} \cong \overline{KL}\)</mcq-option>
</answer>

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Answer:

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<reasoning>

Identify the given congruent parts

Using the Triangle Congruence Postulates knowledge point
Given:
\[

$$\begin{aligned} &\overline{ST} \cong \overline{JK} \quad (\text{Side})\\ &\angle S \cong \angle J \quad (\text{Angle}) \end{aligned}$$

\]

Determine the required side for SAS

Using the Triangle Congruence Postulates knowledge point
\[

$$\begin{aligned} &\text{SAS requires the angle to be included between the two sides.}\\ &\text{For }\Delta STU\text{, }\angle S\text{ is included between }\overline{ST}\text{ and }\overline{SU}.\\ &\text{For }\Delta JKL\text{, }\angle J\text{ is included between }\overline{JK}\text{ and }\overline{JL}.\\ &\text{Therefore, we need: }\overline{SU} \cong \overline{JL} \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>A. \(\overline{TU} \cong \overline{JL}\)</mcq-option>
<mcq-option>B. \(\overline{SU} \cong \overline{KL}\)</mcq-option>
<mcq-correct>C. \(\overline{SU} \cong \overline{JL}\)</mcq-correct>
<mcq-option>D. \(\overline{TU} \cong \overline{KL}\)</mcq-option>
</answer>

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