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itzjustbri
XW and WZ are both congruent, Given.
Angles XWY and ZWY are right angles, Definition of a perpendicular bisector.
YW is congruent to itself, by reflexive property.
Triangles XYW and ZYW are congruent, by SAS.
XY is congruent to ZY, by CPCTC.

Hope this helps :)
akposevictor

Missing statements and reasons in the proof:

  • XW ≅ WZ - Given
  • ∠XWY = ∠ZWY - Def. of a perp. bisector
  • YW ≅ WY - reflexive prop.
  • ΔXYW ≅ ΔZYW - SAS
  • XY ≅ ZY - CPCTC

What is the Side-angle-side Congruence Theorem (SAS)?

The SAS congruence theorem states that if two triangles have two pairs of congruent sides and a pair of included congruent angles, we can prove that both triangles are congruent.

We are given, that XW ≅ WZ.

Also, because YW is perpendicular to XZ, therefore, ∠XWY = ∠ZWY = right angle.

YW ≅ YW by the reflexive property.

This implies that, based on the SAS congruence theorem, we can state that ΔXYW ≅ ΔZYW.

SInce both triangles are congruent, it can then be stated that XY ≅ ZY by CPCTC theorem.

In conclusion, the missing statements and reasons in the proof would be:

Statement 1: XW ≅ WZ (Given)

Statement 2: ∠XWY = ∠ZWY (Definition of a perpendicular bisector)

Statement 3: YW ≅ WY (reflexive property)

Statement 4: ΔXYW ≅ ΔZYW (by SAS congruence theorem)

Statement 5: XY ≅ ZY (by CPCTC)

Learn more about SAS congruence theorem on:

https://brainly.com/question/2102943

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