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Directions: Write the statement or reason in the two-column proof. Use different definitions, postulates, theorems in geometry to suppor given statement. P B Given: TPBA, PR = BC, |TR| > |AC| Prove: mzTPR > mABC Proof: R Statements Reasons 1. TP = BA, PR = BC , |TR| > |AC| 1. Given 2. LTPR = LABC or m2TPR mABC 3. If ZTPR = LABC, then ATPR = AABC. 4. TR AC. 4. 5. The assumption that 5. TR= AC contradicts the given that |TR| > |AC|. LTPR LABC is false. 6. Consider m/TPR |AC. 8. Therefore, mzTPR > mzABC must be 8. Assumption that m/TPR > mLABC is proven to be false. Activity 2: Proving A

Directions: Write the statement or reason in the two-column proof. Use different definitions, postulates, theorems in geometry to suppor given statement. P B Given: TPBA, PR = BC, |TR| > |AC| Prove: mzTPR > mABC Proof: R Statements Reasons 1. TP = BA, PR = BC , |TR| > |AC| 1. Given 2. LTPR = LABC or m2TPR mABC 3. If ZTPR = LABC, then ATPR = AABC. 4. TR AC. 4. 5. The assumption that 5. TR= AC contradicts the given that |TR| > |AC|. LTPR LABC is false. 6. Consider m/TPR |AC. 8. Therefore, mzTPR > mzABC must be 8. Assumption that m/TPR > mLABC is proven to be false. Activity 2: Proving A

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Directions: Write the statement or reason in the two-column proof. Use the different definitions, postulates, theorems in geometry to support the given statement. P B Given: TP BA, PR = BC, |TR| > |AC| Prove: m2TPR > mABC C Proof: R Statements Reasons 1. TP = BA, PR = BC , |TR|> [AC| 1. Given 2. LTPR = LABC or m/TPR <m/ABC. 3. Consider: ZTPR 2. Assumption: mzTPR mLABC 3. LABC. If ZTPR = LABC, then ATPR = AABC. 4. TR= AC. 4. 5. The assumption that 5. TR= AC contradicts the given that TRAC LTPR = LABC is false. 6. Consider m/TPR <m<ABC. 6. If m/TPR <m<BAC, then |TR| <AC. 7. The assumption that m/TPR< 7. |TR| < |AC| contradicts the given that TR>AC m/ABC is 8. Therefore, mzTPR > mzABC must be 8. Assumption that m/TPR > m2ABC is proven to be false. Activity 2: Proving A
Transcribed Image Text:Directions: Write the statement or reason in the two-column proof. Use the different definitions, postulates, theorems in geometry to support the given statement. P B Given: TP BA, PR = BC, |TR| > |AC| Prove: m2TPR > mABC C Proof: R Statements Reasons 1. TP = BA, PR = BC , |TR|> [AC| 1. Given 2. LTPR = LABC or m/TPR <m/ABC. 3. Consider: ZTPR 2. Assumption: mzTPR mLABC 3. LABC. If ZTPR = LABC, then ATPR = AABC. 4. TR= AC. 4. 5. The assumption that 5. TR= AC contradicts the given that TRAC LTPR = LABC is false. 6. Consider m/TPR <m<ABC. 6. If m/TPR <m<BAC, then |TR| <AC. 7. The assumption that m/TPR< 7. |TR| < |AC| contradicts the given that TR>AC m/ABC is 8. Therefore, mzTPR > mzABC must be 8. Assumption that m/TPR > m2ABC is proven to be false. Activity 2: Proving A
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