Flowchart and Paragraph Proofs flowchart proofs The second style of proof is a flowchart proof, which uses boxes and arrows to show the structure of the proof. The steps in a flowchart proof move from left to right, or from top to bottom, shown by the arrows connecting each box. The justification for each step is written below the box. Use the given flowchart proof to write a two-column proof. Given: Prove: Flowchart proof: RS = UV, ST = TU Line RT is congruent to Line TV RS = UV, ST = TU Given RS + ST = TU + UV Add. Prop of = RT = TV Subst. RS +ST = RT,

TU + UV = TV Seg. Add. Post. Line RT is congruent to Line TV Def. of congruent segs. Use the given two-column proof to write a flowchart proof. Given: Prove: Two-colum Proof: Angle 2 is congruent to Angle 4 Measure of Angle 1 = Measure of Angle 3 statements 1. Angle 2 is congruent to Angle 4

2. Angle 1 and Angle 2 are supplementary.

Angle 3 and Angle 4 are supplementary.

3. Angle 1 is congruent to Angle 3

4. Measure of Angle 1 = Measure of Angle 3 Reasons 1. Given

2. Lin. Pair Thm.

3. Congruent Supps. Thm.

4. Def. of congruent angles Paragraph Proofs A paragraph proof is a style of proof that presents the steps of the proof and their matching reasons as sentences in a paragraph. Use the given paragraph proof to write a two-column proof. Given: Prove: Angle WXY is a right angle. Angle 1 is congruent to Angle 3 Angle 1 and Angle 2 are complementary. Paragraph Proof: Since Angle WXY is a right angle, the measure of Angle WXY = 90° by the definition of a right angle. By the Angle Addition Postulate, the measure of Angle WXY = measure of Angle 2 + measure of Angle 3. By substitution, measure of Angle 2 + measure of Angle 3 = 90°. Since Angle 1 is congruent to Angle 3, measure of Angle 1 = measure of Angle 3 by the definition of congruent angles. Using substitution, measure of Angle 2 + measure of Angle 1 = 90°. Thus by the definition of complementary angles, Angle 1 and Angle 2 are complementary. Use the given two-column proof to write a paragraph proof. Given: Prove: Two-column Proof: Angle 1 is congruent to Angle 4 Angle 2 is congruent to Angle 3 Statements 1. Angle 1 is congruent to Angle 4

2. Angle 1 is congruent to Angle 2,

Angle 3 is congruent to Angle 4

3. Angle 2 is congruent to Angle 4

4. Angle 2 is congruent to Angle 3 Reasons 1. Given

2. Vert. Angles Thm.

3. Trans. Prop. of congruent (Steps 1, 2)

4. Trans. Prop. of congruent (Steps 2, 3) Warm-Up 1) 24 percent 2) 28 tires

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# Flowchart and Paragraph Proofs

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