High School

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Based on the diagram below, prove the triangles are congruent by SSS,SAS and ASA.Use the least amount of missing information.

Based on the diagram below prove the triangles are congruent by SSS SAS and ASA Use the least amount of missing information

Answer :

1. SSS: [tex]\(\overline{LK} \cong \overline{VU}\)[/tex], [tex]\(\overline{KJ} \cong \overline{UT}\)[/tex], [tex]\(\overline{LJ} \cong \overline{VT}\)[/tex]

2. SAS: [tex]\(\overline{LK} \cong \overline{VU}\)[/tex], [tex]\(\overline{KJ} \cong \overline{UT}\)[/tex], [tex]\(\angle K \cong \angle U\)[/tex]

3. ASA: [tex]\(\overline{LK} \cong \overline{VU}\)[/tex], [tex]\(\overline{KJ} \cong \overline{UT}\)[/tex], [tex]\(\angle L \cong \angle V\)[/tex].

For SSS (Side-Side-Side) congruence, have all three sides of one triangle congruent to the corresponding sides of the other triangle.

Given:

[tex]\(\overline{LK} \cong \overline{VU}\)[/tex] and [tex]\(\overline{KJ} \cong \overline{UT}\)[/tex].

For SAS (Side-Angle-Side) congruence, two sides are needed and the included angle of one triangle congruent to the corresponding sides and the included angle of the other triangle.

Given:

[tex]\(\overline{LK} \cong \overline{VU}\)[/tex] and [tex]\(\overline{KJ} \cong \overline{UT}\)[/tex], and [tex]\(\angle K \cong \angle U\)[/tex].

For ASA (Angle-Side-Angle) congruence, two angles are needed and the included side of one triangle congruent to the corresponding angles and the included side of the other triangle.

Given:

[tex]\(\overline{LK} \cong \overline{VU}\)[/tex] and [tex]\(\overline{KJ} \cong \overline{UT}\)[/tex], and [tex]\(\angle L \cong \angle V\)[/tex].

So, the missing information for each case is:

1. SSS: [tex]\(\overline{LJ} \cong \overline{VT}\)[/tex]

2. SAS: [tex]\(\angle K \cong \angle U\)[/tex]

3. ASA: [tex]\(\angle L \cong \angle V\)[/tex].

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Rewritten by : Barada