Directions: Write the statement or reason in the two-column proof. Use thedifferent definitions, postulates, theorems in geometry to support thegiven statement.PBGiven: TP BA, PR = BC, |TR| > |AC|Prove: m2TPR > mABCCProof:RStatementsReasons1. TP = BA, PR = BC , |TR|> [AC|1. Given2. LTPR = LABC or m/TPR ACm/ABC is8. Therefore, mzTPR > mzABC must be8. Assumption that m/TPR > m2ABCis proven to be false.Activity 2: ProvingA

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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

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter2: Parallel Lines

Section2.2: Indirect Proof

Problem 12E: Which of the following statements would you prove by the indirect method? a If ACAB in ABC, then...

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Question

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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