in a triangle where there told to solve <T ≅ <S they make the following chart Statements: 1.line RU Bisects <SRT 2. Line RS ≅ line RT 3. <SRU ≅ <TRU 4. line RU ≅ line RU 5. triangleRSU ≅ triangleRTU 6. <T ≅ <A and for their reasons: 1. Given 2. Given 3. Definition of angle bisector 4. Reflexive property of congruence 5. a. 6. b. state the reasons for a and b

Question

in a triangle where there told to solve <T ≅ <S they make the following chart Statements: 1.line RU Bisects <SRT 2. Line RS ≅ line RT 3. <SRU ≅ <TRU 4. line RU ≅ line RU 5. triangleRSU ≅ triangleRTU 6. <T ≅ <A and for their reasons: 1. Given 2. Given 3. Definition of angle bisector 4. Reflexive property of congruence 5. a. 6. b. state the reasons for a and b

Answer 1

Reason for statement 5a: SAS (side-angle-side) congruence postulate. This is because line RS is congruent to line RT (given in statement 2), angle SRU is congruent to angle TRU (given in statement 3), and line RU is congruent to itself (reflexive property in statement 4).

Reason for statement 5b: CPCTC (corresponding parts of congruent triangles are congruent) theorem. This is because triangle RSU is congruent to triangle RTU (statement 5a) and triangle RUS is congruent to triangle RUT (congruence is symmetric), so the corresponding angles T and A are congruent.