Question

The proof that UX ≅ SV is shown.

Given: △STU an equilateral triangle

∠TXU ≅ ∠TVS

Prove: UX ≅ SV

Triangle T X V is shown. Point S is on side T X and point U is on side T V. A line is drawn from points S to U to form equilateral triangle T S U. Lines are drawn from point S to point V and from point U to point X and intersect at point W.

What is the missing statement in the proof?

Statement
Reason
1. ∠TXU ≅ ∠TVS 1. given
2. ∠STV ≅ ∠UTX 2. reflex. prop.
3. △STU is an equilateral triangle 3. given
4. ST ≅ UT 4. sides of an equilat. △ are ≅
5. ? 5. AAS
6. UX ≅ SV 6. CPCTC

Options
△SXU ≅ △TVS
△UVX ≅ △SXV
△SWX ≅ △UWV
△TUX ≅ △TSV

Answer 1

Explanation:

To prove UX ≅ SV based on the given information, we need to complete the missing statement in the proof. Let's analyze the given information and options to find the correct missing statement.

Given:

- Triangle STU is an equilateral triangle.

- ∠TXU ≅ ∠TVS.

We are trying to prove UX ≅ SV.

Let's consider the options provided:

Option A: △SXU ≅ △TVS

Option B: △UVX ≅ △SXV

Option C: △SWX ≅ △UWV

Option D: △TUX ≅ △TSV

To determine the missing statement, we need to find congruent triangles that involve UX and SV. Looking at the given triangle and the angles given, we observe that ∠TXU and ∠TVS are corresponding angles.

Corresponding angles suggest that triangles TUX and TVS have a congruent angle pair. Thus, we can determine that the missing statement is:

**Option D: △TUX ≅ △TSV**

Let's review the proof now:

Statement | Reason

1. ∠TXU ≅ ∠TVS | Given

2. ∠STV ≅ ∠UTX | Reflexive property

3. △STU is an equilateral triangle | Given

4. ST ≅ UT | Sides of an equilateral triangle are congruent

5. △TUX ≅ △TSV | AAS (Angle-Angle-Side)

6. UX ≅ SV | CPCTC (Corresponding Parts of Congruent Triangles are Congruent)

Therefore, the missing statement in the proof is: **△TUX ≅ △TSV**.