Similar Triangles Exercises

What is the reason for statement 1?

What is the reason for statement 2?

What is the reason for statement 3?

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)

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.	?

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)

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	?

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.	?

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

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	?