Question

digital textbook
click each link below to learn the concepts. each component includes a video and you can select your desired language.
student fl geometry -> triangle congruence -> proving triangles congruent -> 5.6.2 guided instruction
student fl geometry -> triangle congruence -> proving triangles congruent -> 5.6.3 guided practice
then, answer check your understanding assignment below. you have three attempts.
given: \\( \angle w d s \cong \angle k d s \\), d is the midpoint of \\( \overline{w k} \\)
prove: \\( \triangle s d w \cong \triangle s d k \\)
complete the paragraph proof.
it is given that d is the midpoint of \\( \overline{w k} \\), so \\( \overline{w d} \cong \overline{k d} \\) by the. it is also given that
\\( \angle w d s \cong \angle k d s \\). \\( \overline{s d} \cong \overline{s d} \\) by the. therefore, \\( \triangle s d w \cong \triangle s d k \\) by

Explanation:

Step1: Midpoint Definition

A midpoint of a segment divides the segment into two congruent parts. So, if \(D\) is the midpoint of \(\overline{WK}\), then \(\overline{WD}\cong\overline{KD}\) by the definition of a midpoint.

Step2: Reflexive Property

For any segment \(\overline{AB}\), \(\overline{AB}\cong\overline{AB}\). So, \(\overline{SD}\cong\overline{SD}\) by the reflexive property of congruence.

Step3: SAS Congruence Criterion

The Side - Angle - Side (SAS) 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 two triangles are congruent. Here, we have \(\overline{WD}\cong\overline{KD}\), \(\angle WDS\cong\angle KDS\), and \(\overline{SD}\cong\overline{SD}\). So, \(\triangle SDW\cong\triangle SDK\) by SAS.

Answer:

First blank: definition of a midpoint; Second blank: reflexive property of congruence; Third blank: SAS