1. Given: 𝑈𝐵 𝑖𝑠 𝑎 𝑚𝑒𝑑𝑖𝑎𝑛 𝑡𝑜 𝐶𝑆 𝑈𝐶 ≅ 𝑈𝑆 5. 𝑈𝐵 ≅ 𝑈𝐵C 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

2. 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

3. Proving Triangles Congruent
Mixed Problems

4. 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

5. 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

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

7. 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

8. 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

9. 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

10. 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