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snow_tiger [21]
3 years ago
7

The proof that UX ≅ SV is shown. Given: △STU an equilateral triangle ∠TXU ≅ ∠TVS Prove: UX ≅ SV 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
Mathematics
2 answers:
iren2701 [21]3 years ago
6 0
Triangle STU is congruent to triangle UTX is the missing step. AAS (angle-angle-side) is a method of proving 2 triangles congruent, and using the already proved information, you can find the triangles that are congruent by AAS.
Tanzania [10]3 years ago
6 0

Answer:

5. Statement: \triangle TXU\cong \triangle TSV

Step-by-step explanation:

Given, triangle STU is an equilateral triangle.

\angle TXU \cong \angle TVS

To prove that UX \cong SV

Proof:

1. Statement: \angle TXU \cong \angle TVS

Reason: Given in question .

2. Statement: \angle STV \cong \angle UTX

Reason: By using reflection proeperty of rotation.

3. Statement: \triangle STU is an equilateral triangle.

Reason: \angle STU= \angle TSU=\angle SUT given.

4. Statement: ST \cong UT

Reason: Sides of equilateral triangle STU.

5. \tringle TXU \cong \triangle TSV

Reason: AAS congruence property of triangle.

6. Statement: UX\cong SV

Reason: CPCT ( corresponding parts of congruence triangles).

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