Question

example 1
triangles obw and wty are shown.
a. mark the image with the given information:
\\( \overline { o w } \cong \overline { y w } \\) , \\( \overline { o b } \cong \overline { t y } \\) , and \\( \angle o b w \cong \angle t y w \\)
b. what other parts can be marked on this image?
c. is \\( \triangle o b w \cong \triangle w t y \\) ? if yes, which postulate / theorem
supports this?
example 2 | part 1 - you try!
a. mark the image with the given information:
\\( \overline { e q } \cong \overline { e m } \\) and \\( \angle k e q \cong \angle k e m \\)
b. what other parts can be marked on this imag
c. is \\( \triangle k e k \cong \triangle m e k \\) ? if yes, which postulate / tr
supports this?
example 2 | part 2 - lets discuss
fill in the blanks.
it is given that \\( \overline { e q } \cong \overline { e m } \\) and \\( \angle k e q \cong \angle k e m \\) . by the reflexive property, __________________________.
therefore, \\( \triangle k e k \cong \triangle m e k \\) by ______________.

Explanation:

Step1: Use reflexive property

By the reflexive property, \(\overline{KE}\cong\overline{KE}\).

Step2: Determine congruence postulate

We have \(\overline{EQ}\cong\overline{EM}\), \(\angle KEQ\cong\angle KEM\), and \(\overline{KE}\cong\overline{KE}\). So, \(\triangle KEQ\cong\triangle KEM\) by \(SAS\) (Side - Angle - Side) postulate.

Answer:

By the reflexive property, \(\overline{KE}\cong\overline{KE}\). Therefore, \(\triangle KEQ\cong\triangle KEM\) by \(SAS\) (Side - Angle - Side) postulate.