Question

1. mark the given information and any parts on the triangles that you can prove congruent and determine how the triangles are congruent. a) sss ≅ b) sas ≅ c) asa ≅ d) aas ≅ e) as are not ≅ 8) mark any congruent parts you can prove on the triangles. which of the following is the correct congruence statement for the given triangles? a) △abc ≅ △dbc b) △abc ≅ △dcb c) △abc ≅ △bdc d) △abc ≅ △acbd 9) mark any congruent parts you can prove on the triangles. what additional piece of information is required in order to prove the triangles congruent by asa? a) st ≅ dt b) ud ≅ us c) ∠d ≅ ∠s d) ∠dtu ≅ ∠stu

Explanation:

7)

Step1: Recall congruence criteria

We know the congruence criteria: SSS (Side - Side - Side), SAS (Side - Angle - Side), ASA (Angle - Side - Angle), AAS (Angle - Angle - Side).

Step2: Analyze the given triangle parts

In the given figure, we have two angles (marked in yellow) and a non - included side (the side common to both triangles). The AAS (Angle - Angle - Side) 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.

Step1: Check triangle congruence

For triangles \(\triangle ABC\) and \(\triangle DCB\), we have \(AB = DC\) (given by the marks on the sides), \(AC=DB\) (given by the marks on the sides), and \(BC = CB\) (common side). By the SSS (Side - Side - Side) congruence criterion \(\triangle ABC\cong\triangle DCB\).

Step1: Recall ASA criterion

The ASA (Angle - Side - Angle) criterion requires two angles and the included side. We already have two angles (the ones marked at \(U\) and \(T\)). For ASA, we need the included side. If \(\angle D\cong\angle S\), along with the two angles at \(U\) and \(T\) and the side \(UT\) (common side), we can use ASA.

Answer:

D) \(AAS\cong\)

8)