Given: 𝑈𝐵 𝑖𝑠 𝑎 𝑚𝑒𝑑𝑖𝑎𝑛 𝑡𝑜 𝐶𝑆 𝑈𝐶 ≅ 𝑈𝑆 5. 𝑈𝐵 ≅ 𝑈𝐵 C U S B Statement Reason 1. 𝑈𝐵 𝑖𝑠 𝑎 𝑚𝑒𝑑𝑖𝑎𝑛 𝑡𝑜 𝐶𝑆 1. Given 2. 𝑈𝐶 ≅ 𝑈𝑆 2. Given 3.𝐵 𝑖𝑠 𝑡ℎ𝑒 𝑚𝑖𝑑𝑝𝑜𝑖𝑛𝑡 𝑜𝑓 𝐶𝑆 3. A median extends from the vertex of a triangle to the midpoint of the opposite side 4. A midpoint divides a segment into two congruent parts 4. 𝐶𝐵 ≅ 𝑆𝐵 Given: 𝑈𝐵 𝑖𝑠 𝑎 𝑚𝑒𝑑𝑖𝑎𝑛 𝑡𝑜 𝐶𝑆 𝑈𝐶 ≅ 𝑈𝑆 5. 𝑈𝐵 ≅ 𝑈𝐵 5. Reflexive Postulate Prove: ∆𝐶𝑈𝐵≅∆𝑆𝑈𝐵 6. ∆𝐶𝑈𝐵≅∆𝑆𝑈𝐵 6. SSS ≅ SSS

K Statement Reason 1. 𝐿𝐴 ≅ 𝑅𝐸 E 2. 𝐴𝐾 ≅ 𝐸𝐾 A 1. 𝐿𝐴 ≅ 𝑅𝐸 1. Given E 2. 𝐴𝐾 ≅ 𝐸𝐾 2. Given A 3. 𝑆 𝑖𝑠 𝑡ℎ𝑒 𝑚𝑖𝑑𝑝𝑜𝑖𝑛𝑡 𝑜𝑓 𝐿𝑅 3. Given 4. 𝐿𝐴 + 𝐴𝐾 ≅ 𝑅𝐸 + 𝐸𝐾 4. Addition Postulate 5. 𝐿𝐴 + 𝐴𝐾 ≅ 𝐿𝐾 𝑅𝐸 + 𝐸𝐾 ≅ 𝑅𝐾 5. Partition Postulate L S R 6. 𝐿𝐾 ≅ 𝑅𝐾 6. Substitution Postulate 7. 𝐿𝑆 ≅ 𝑆𝑅 7. A midpoint divides a segment into two congruent parts Given: 𝐿𝐴 ≅ 𝑅𝐸 𝐴𝐾 ≅ 𝐸𝐾 𝑆 𝑖𝑠 𝑡ℎ𝑒 𝑚𝑖𝑑𝑝𝑜𝑖𝑛𝑡 𝑜𝑓 𝐿𝑅 8. 𝑆𝐾 ≅ 𝑆𝐾 8. Reflexive Postulate Prove: ∆𝐿𝐾𝑆≅∆𝑅𝐾𝑆 9. ∆𝐿𝐾𝑆≅∆𝑅𝐾𝑆 9. SSS ≅ SSS

Proving Triangles Congruent Mixed Problems

Statement Reason 1. Given 2. Given Pg. 7 #1 Statement Reason 1. Given 2. Given 3. A midpoint divides a segment into two congruent parts 4. Two adjacent angles that form a straight line are a linear pair 5. Linear pairs are supplementary 6. Supplements of congruent angles are congruent 7. Vertical angles are congruent

Statement Reason 1. Given 2. Given 3. Given 4. Given Pg. 7 #2 Statement Reason 1. Given 2. Given 3. Given 4. Given 5. Perpendicular segments form right angles 6. All right angles are congruent 7. Reflexive postulate 8. Subtraction Postulate 9. Partition Postulate 10. Substitution Postulate

Pg. 7 #3 Statement Reason 1. Given 2. Given 3. Reflexive postulate

Statement Reason 1. Given 2. Given Pg. 7 #4 Statement Reason 1. Given 2. Given 3. A median extends from a vertex to a midpoint of the opposite side of a triangle. 4. A midpoint divides a segment into two congruent parts 5. Reflexive postulate

Statement Reason 1. Given 2. Given 3. Given Pg. 7 #5 Statement Reason 1. Given 2. Given 3. Given 4. A median extends from a vertex to a midpoint of the opposite side of a triangle. 5. A midpoint divides a segment into two congruent parts 6. Addition Postulate 7. Partition Postulate 8. Substitution Postulate 9. Reflexive postulate

Statement Reason 1. Given 2. Given 3. Given 4. Given Pg. 7 #7 Statement Reason 1. Given 2. Given 3. Given 4. Given 5. A midpoint divides a segment into two congruent parts 6. Substitution postulate

Statement Reason 1. Given 2. Given 3. Given Pg. 7 #8 Statement Reason 1. Given 2. Given 3. Given 4. A segment bisector divides a segment into two congruent parts 5. Perpendicular segments form right angles 6. All right angles are congruent 7. Subtraction Postulate 8. Partition Postulate 9. Substitution Postulate