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Discovering! This part consists of proving activities for the 6 theorems on triangle inequalities. Analyze and use the hint provided in each activity to complete the proof. Note that inequalities in triangles, even without actual measurements, can be justified deductively using theorems on inequalities in triangles. Activity 1 Directions: Complete the proof of Triangle Inequality Theorem 1(Ss→Aa) in two- column form by choosing the right statement written in the box below. Write your answer in a separate sheet of paper. PQ = PS Angle Addition Postulate Property of Inequality m22 = M2PRQ + m23 41 22 m22 > M2QRP MLQSR + MZPRQ +mz3 = 180° M2PQR > M2PRQ Substitution Property APQS is isosceles triangle P. Given: APQR; |PR| > |PQ| Prove: mzQ > mzR R Q Proof: We cannot directly prove that mzQ > mzR, thus, there is a need to make additional constructions (see the second figure). Locate S on PR such that |PS = |PQI, and connect S to Q with a segment to form a triangle PQS. Statements Reasons 1. (How do you describe the relationship 1. By construction between PQ and PS ?) 2. (Based on statement 1, what kind of 2. Definition of isosceles triangle a triangle is APQS?) 3. (Based on statement 1, how do you 3. Base angles of isosceles triangles are describe the relationship between 21 and 22?) 4. mzQ = mz1+ m23 congruent. 4. (What postulate supports the statement that the sum of the measures of 41 and 43 is equal to measure of ¿PQR?)

Discovering! This part consists of proving activities for the 6 theorems on triangle inequalities. Analyze and use the hint provided in each activity to complete the proof. Note that inequalities in triangles, even without actual measurements, can be justified deductively using theorems on inequalities in triangles. Activity 1 Directions: Complete the proof of Triangle Inequality Theorem 1(Ss→Aa) in two- column form by choosing the right statement written in the box below. Write your answer in a separate sheet of paper. PQ = PS Angle Addition Postulate Property of Inequality m22 = M2PRQ + m23 41 22 m22 > M2QRP MLQSR + MZPRQ +mz3 = 180° M2PQR > M2PRQ Substitution Property APQS is isosceles triangle P. Given: APQR; |PR| > |PQ| Prove: mzQ > mzR R Q Proof: We cannot directly prove that mzQ > mzR, thus, there is a need to make additional constructions (see the second figure). Locate S on PR such that |PS = |PQI, and connect S to Q with a segment to form a triangle PQS. Statements Reasons 1. (How do you describe the relationship 1. By construction between PQ and PS ?) 2. (Based on statement 1, what kind of 2. Definition of isosceles triangle a triangle is APQS?) 3. (Based on statement 1, how do you 3. Base angles of isosceles triangles are describe the relationship between 21 and 22?) 4. mzQ = mz1+ m23 congruent. 4. (What postulate supports the statement that the sum of the measures of 41 and 43 is equal to measure of ¿PQR?)

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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Statements Reasons (What property supports the inequality statement focusing on L1 based on statement 4?) 6. 6. mzQ > mz2 (What property supports the step where the right side of the inequality in statement 5 is replaced with its equivalent in statement 3?) 7. (Based on the illustration, write an operation statement involving measures of ZQSR,LR, and43. 7. The sum of the measures of the interior angles of a triangle is 180° 8. Linear pair theorem 8. m22+ M2QSR = 180° 9. m22+ M2QSR MLQSR+mzR +mL3 9. Substitution/ Transitive Property %3D 10. (What will be the result if mzQSR is subtracted from both sides of statement 9?) 10. Subtraction Property 11. (Based on statement number 10, write an inequality statement focusing on ZR.) 11. Property of Inequality 12. 12. Transitive Property (Based on statements 6 and 11: If MLPQR > mL2 and m22 >mLR, then
Transcribed Image Text:Statements Reasons (What property supports the inequality statement focusing on L1 based on statement 4?) 6. 6. mzQ > mz2 (What property supports the step where the right side of the inequality in statement 5 is replaced with its equivalent in statement 3?) 7. (Based on the illustration, write an operation statement involving measures of ZQSR,LR, and43. 7. The sum of the measures of the interior angles of a triangle is 180° 8. Linear pair theorem 8. m22+ M2QSR = 180° 9. m22+ M2QSR MLQSR+mzR +mL3 9. Substitution/ Transitive Property %3D 10. (What will be the result if mzQSR is subtracted from both sides of statement 9?) 10. Subtraction Property 11. (Based on statement number 10, write an inequality statement focusing on ZR.) 11. Property of Inequality 12. 12. Transitive Property (Based on statements 6 and 11: If MLPQR > mL2 and m22 >mLR, then
What's Neuw Discovering! This part consists of proving activities for the 6 theorems on triangle inequalities. Analyze and use the hint provided in each activity to complete the proof. Note that inequalities in triangles, even without actual measurements, can be justified deductively using theorems on inequalities in triangles. Activity 1 Directions: Complete the proof of Triangle Inequality Theorem 1(Ss→Aa) in two- column form by choosing the right statement written in the box below. Write your answer in a separate sheet of paper. PQ = PS MLPQR > MLPRQ Angle Addition Postulate Property of Inequality m22 = M2PRQ + mz3 21 = L2 m22 > M2QRP MLQSR + MZPRQ +mz3 = 180° APQS is isosceles triangle Substitution Property P. P. Given: APQR;|PR| > |PQ| Prove: mzQ > mzR R Q Proof: We cannot directly prove that mzQ > mzR, thus, there is a need to make additional constructions (see the second figure). Locate S on PR such that |PS = |PQI, and connect S to Q with a segment to form a triangle PQS. Statements Reasons 1. (How do you describe the relationship 1. By construction between PQ and PS ?) 2. (Based on statement 1, what kind of 2. Definition of isosceles triangle a triangle is APOS?) 3. (Based on statement 1, how do you 3. Base angles of isosceles triangles are describe the relationship between 21 and 22?) 4. mzQ = mz1+ mz3 congruent. 4. (What postulate supports the statement that the sum of the measures of 21 and 23 is equal to measure of LPQR?) 5. mzQ > mz1 5.
Transcribed Image Text:What's Neuw Discovering! This part consists of proving activities for the 6 theorems on triangle inequalities. Analyze and use the hint provided in each activity to complete the proof. Note that inequalities in triangles, even without actual measurements, can be justified deductively using theorems on inequalities in triangles. Activity 1 Directions: Complete the proof of Triangle Inequality Theorem 1(Ss→Aa) in two- column form by choosing the right statement written in the box below. Write your answer in a separate sheet of paper. PQ = PS MLPQR > MLPRQ Angle Addition Postulate Property of Inequality m22 = M2PRQ + mz3 21 = L2 m22 > M2QRP MLQSR + MZPRQ +mz3 = 180° APQS is isosceles triangle Substitution Property P. P. Given: APQR;|PR| > |PQ| Prove: mzQ > mzR R Q Proof: We cannot directly prove that mzQ > mzR, thus, there is a need to make additional constructions (see the second figure). Locate S on PR such that |PS = |PQI, and connect S to Q with a segment to form a triangle PQS. Statements Reasons 1. (How do you describe the relationship 1. By construction between PQ and PS ?) 2. (Based on statement 1, what kind of 2. Definition of isosceles triangle a triangle is APOS?) 3. (Based on statement 1, how do you 3. Base angles of isosceles triangles are describe the relationship between 21 and 22?) 4. mzQ = mz1+ mz3 congruent. 4. (What postulate supports the statement that the sum of the measures of 21 and 23 is equal to measure of LPQR?) 5. mzQ > mz1 5.
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