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. 1. \\( \overline{\mathrm{kw}} \\) bisects \\( \overline{\mathrm{rd}}, \overline{\mathrm{kr}} \cong \overline{\mathrm{kd}} \\) 1. given 2. \\( \mathrm{rw}=\mathrm{dw} \\) 2. 3. \\( \overline{\mathrm{rw}} \cong \overline{\mathrm{dw}} \\) 3. 4. \\( \overline{\mathrm{kw}} \cong \overline{\mathrm{kw}} \\) 4. 5. \\( \triangle \mathrm{rkw} \cong \triangle \mathrm{dkw} \\) 5.

Explanation:

Step1: Definition of bisector

If a line bisects a segment, it divides the segment into two equal parts. So, if \(\overline{KW}\) bisects \(\overline{RD}\), then \(RW = DW\) (by the definition of a segment bisector).

Step2: Congruent segments from equal lengths

If \(RW = DW\), then \(\overline{RW}\cong\overline{DW}\) (by the definition of congruent segments: segments that have the same length are congruent).

Step3: Reflexive property

For any segment \(\overline{AB}\), \(\overline{AB}\cong\overline{AB}\). So, \(\overline{KW}\cong\overline{KW}\) by the reflexive property of congruence (a segment is congruent to itself).

Step4: SSS (Side - Side - Side) congruence criterion

We have \(\overline{KR}\cong\overline{KD}\) (given), \(\overline{RW}\cong\overline{DW}\) (from step 2), and \(\overline{KW}\cong\overline{KW}\) (from step 3). So, \(\triangle RKW\cong\triangle DKW\) by the SSS (Side - Side - Side) congruence criterion (if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent).

Answer:

1. Definition of segment bisector; 3. Definition of congruent segments; 4. Reflexive property of congruence; 5. SSS (Side - Side - Side)