Question

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2. Use the figure to answer the questions below. (see attachment)

a. Stephan says that ΔXWV ≅ ΔUWS by the SAS congruence postulate.
Do you Agree or Disagree?
Justify your decision.
Hint: State if you agree or disagree.
- If you agree, identify the congruent corresponding parts that prove your opinion and the reason you know they are congruent.
- If you disagree, identify the existing congruent corresponding parts and the part(s) that are needed but not provided to prove the triangles congruent using SAS.




b. Suppose that it is also known that ∠V≅∠S.
Which postulate or theorem can be used to prove that ΔXWV ≅ ΔUWS?
Justify your decision.
Hint: Provide the name of the congruence postulate or theorem.
- Then, identify the existing congruent corresponding parts and the reason you know they are congruent.
- However, if you think there is not enough information to prove the triangles congruent, identify the existing congruent corresponding parts and the part(s) that are needed but not provided.

Answer 1

a. Disagree because the existing congruent corresponding parts are:

VW = SW

m∠ VWX = m∠ SWV

not enough to prove that Δ XWV ≅ Δ UWS

The part that needed but not provided to prove the triangles

congruent using SAS is XW = UW

b. Δ XWV ≅ Δ UWS by ASA postulate

Step-by-step explanation:

Let us revise the cases of congruence

1. SSS  ⇒ 3 sides in the 1st Δ ≅ 3 sides in the 2nd Δ

2. SAS ⇒ 2 sides and including angle in the 1st Δ ≅ 2 sides and

    including angle in the 2nd Δ

3. ASA ⇒ 2 angles and the side whose joining them in the 1st Δ

     ≅ 2 angles and the side whose joining them in the 2nd Δ

4. AAS ⇒ 2 angles and one side in the 1st Δ ≅ 2 angles  and one side

   in the 2nd Δ

In the attached figure there are two triangles

Δ XWV and Δ UWS

∵ VW = SW ⇒ given

∵ m∠VWX = m∠SWV ⇒ vertical opposite angles

- To prove that the two triangles are congruent we must have a third

  condition like

   XW = UW ⇒ SAS OR

   m∠V = m∠S ⇒ ASA OR

   m∠X = m∠U ⇒ AAS

∵ There is no other given help us to prove that the 2Δs are congruent

∴ I disagree with him because we must have one another condition

 that XW= WU with the given conditions to prove that ΔXWV ≅ ΔUWS

  By SAS postulate

a.

Disagree because the existing congruent corresponding parts are:

VW = SW

m∠VWX = m∠SWV

not enough to prove that ΔXWV ≅ ΔUWS

The part that needed but not provided to prove the triangles

congruent using SAS is XW = UW

b.

∵ m∠V = m∠S ⇒ given

∵ VW = SW ⇒ given

∵ m∠VWX = m∠SWV ⇒ vertical opposite angles

- 2 angles and the side whose joining them in Δ  XWV ≅ 2 angles and

  the side whose joining them in the Δ  UWS

∴ ΔXWV ≅ ΔUWS ⇒ ASA postulate

ΔXWV ≅ ΔUWS by ASA postulate

Learn more:

You can learn more about congruence postulate of Δs in brainly.com/question/3202836

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