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# Parallel Lines and Congruent Angles: Proving the Equality of Segments in Parallelogram RSTU

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Question: Parallelogram RSTU is shown below. Ilan needs to prove that RS¯¯¯¯¯≅TU¯¯¯¯¯ and RU¯¯¯¯¯≅TS¯¯¯¯¯ . His proof is shown in the table below. Step Statement 1 RSTU is a parallelogram 2 RS¯¯¯¯¯ is parallel to TU¯¯¯¯¯ and RU¯¯¯¯¯ is parallel to TS¯¯¯¯¯ 3 ∠RSU≅∠TUS and ∠RUS≅∠TSU 4 SU¯¯¯¯¯≅US¯¯¯¯¯ 5 △RSU≅△TUS 6 RS¯¯¯¯¯≅TU¯¯¯¯¯ and RU¯¯¯¯¯≅TS¯¯¯¯¯ Select ALL reasons that support one or more statements in the proof. symmetric property definition of a parallelogram alternate interior angles are congruent opposite sides of a parallelogram are congruent corresponding parts of congruent triangles are congruent

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The reasons that support one or more statements in the proof are: - Definition of a parallelogram (Supports Step 2. In a parallelogram, opposite sides are parallel) - Alternate interior angles are congruent (Supports Step 3. When lines are parallel, alternate interior angles are congruent) - Opposite sides of a parallelogram are congruent (Supports Step 1 and Step 6. In a parallelogram, opposite sides are congruent) - Corresponding parts of congruent triangles are congruent (Supports Step 6. If triangles are congruent, all corresponding parts including sides and angles are congruent) The symmetric property doesn't directly support any of the statements in the proof.

Jan. 12, 2024, 8:22 a.m.

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