Question

w is the midpoint of \\( \overline { u v } \\). complete the proof that \\( \overline { t v } \cong \overline { t u } \\).

Explanation:

Step1: Definition of midpoint

Given in the problem.

Step2: Definition of perpendicular

Shown by the right - angle symbol.

Step3: Definition of perpendicular

If two lines are perpendicular, the angles formed are right angles, and all right angles are congruent.

Step4: Definition of midpoint

A midpoint divides a segment into two congruent segments.

Step5: Reflexive property of congruence

Any segment is congruent to itself.

Step6: SAS (Side - Angle - Side) Congruence Postulate

Two triangles are congruent if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle. Here, \(\overline{UW}\cong\overline{VW}\), \(\angle TWU\cong\angle TWV\), \(\overline{TW}\cong\overline{TW}\).

Step7: CPCTC (Corresponding Parts of Congruent Triangles are Congruent)

If two triangles are congruent, then their corresponding parts are congruent.

Answer:

1. Given
2. Definition of perpendicular
3. All right angles are congruent
4. Definition of midpoint
5. Reflexive property of congruence
6. SAS Congruence Postulate
7. CPCTC