Question

state what additional information is required in order to know that the triangles are congruent for the reason given.

1. asa
2. sss
3. sas
4. aas

5)____
6)____
7)____
8)____

Explanation:

5. ASA (Angle - Side - Angle)

ASA congruence criterion states that if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the two triangles are congruent.
We already have \( \angle DTU=\angle STU\) (given as marked angles) and \( UT = UT\) (common side). So we need \( \angle DUT=\angle SUT\)

6. SSS (Side - Side - Side)

SSS congruence criterion states that if three sides of one triangle are equal to three sides of another triangle, then the two triangles are congruent.
We already have \( RQ = SD\) (given as marked equal sides). We also know \( QS=QS\) (common side). So we need \( RS = QD\)

7. SAS (Side - Angle - Side)

SAS congruence criterion states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the two triangles are congruent.
We already have \( UV = KM\) (given as marked equal sides). Also, \( \angle UVW=\angle KMH\) (vertical angles are equal). So we need \( VW = MH\)

8. AAS (Angle - Angle - Side)

AAS congruence criterion states that if two angles and a non - included side of one triangle are equal to two angles and the corresponding non - included side of another triangle, then the two triangles are congruent.
We already have \( \angle QDC=\angle EDC\) (given as marked angles). Also, \( CD = CD\) (common side). So we need \( \angle Q=\angle E\)

Answer:

1. \( \angle DUT=\angle SUT\)
2. \( RS = QD\)
3. \( VW = MH\)
4. \( \angle Q=\angle E\)