Example 1
What is the reason for statement 1?
| Statement | Reason |
| 1. ∠B ≅ ∠K | ? |
Example 2
What is the reason for statement 2?
| Statement | Reason |
| 1. ∠B ≅ ∠K | Given (in figure) |
| 2. ∠BIR ≅ ∠KIC | ? |
Example 3
What is the reason for statement 3?
| Statement | Reason |
| 1. ∠B ≅ ∠K | Given (in figure) |
| 2. ∠BIR ≅ ∠KIC | Vertical angles theorem |
| 3. ∆BRI ~ ∆KCI | ? |
Example 4
What is statement 2?
Given: A, S, and E are the midpoints on their respective sides of ∆BKT.
Prove: ∆BKT ~ ∆ESA
| Statement | Reason |
| 1. A is the midpoint of BK, S is the midpoint of BT, and E is the midpoint of KT | Given |
2.  | Triangle Midsegment Theorem (1) |
Example 5
What is the reason for statement 3?
Given: A, S, and E are the midpoints on their respective sides of ∆BKT.
Prove: ∆BKT ~ ∆ESA
| Statement | Reason |
| 1. A is the midpoint of BK, S is the midpoint of BT, and E is the midpoint of KT | Given |
2.  | Triangle Midsegment Theorem (1) |
3.  | ? |
Example 6
What is statement 4?
Given: A, S, and E are the midpoints on their respective sides of ∆BKT.
Prove: ∆BKT ~ ∆ESA
| Statement | Reason |
| 1. A is the midpoint of BK, S is the midpoint of BT, and E is the midpoint of KT | Given |
2.  | Triangle Midsegment Theorem (1) |
3.  | Triangle Midsegment Theorem (1) |
| 4. SE = ? | Triangle Midsegment Theorem (1) |
Example 7
What is the reason for statement 6?
Given: A, S, and E are the midpoints on their respective sides of ∆BKT.
Prove: ∆BKT ~ ∆ESA
| Statement | Reason |
| 1. A is the midpoint of BK, S is the midpoint of BT, and E is the midpoint of KT | Given |
2.  | Triangle Midsegment Theorem (1) |
3.  | Triangle Midsegment Theorem (1) |
4.  | Triangle Midsegment Theorem (1) |
5.  | Statements 2, 3, 4 |
| 6. ∆BKT ~ ∆ESA | ? |
Example 8
Using the image below, we want to prove that ∆QET ~ ∆UES. What is the reason for statement 2?
| Statement | Reason |
| 1. QT || US | Given |
2.  | ? |
Example 9
Using the image below, we want to prove that ∆QET ~ ∆UES. What is statement 3?
| Statement | Reason |
| 1. QT || US | Given |
2.  | Triangle Proportionality Theorem |
| 3. ? | Reflexive Property |
Example 10
Using the image below, we want to prove that ∆QET ~ ∆UES. What is the reason for statement 4?
| Statement | Reason |
| 1. QT || US | Given |
| 2. | Triangle Proportionality Theorem |
| 3. ∠QET ≅ ∠UES | Reflexive Property |
| 4. ∆ QET ~ ∆UES | ? |