Question

Use the diagram to complete the table.



Question
Move statements into the table to prove that triangle Q R S is an isosceles triangle.

Response area with 4 blank spaces
line R T is parallel to segment Q S Given
angle W R T is congruent to angle R S Q Given
Blank space 1 empty
​

Definition of transversal line
Blank space 2 empty
​

Corresponding Angles Theorem
Blank space 3 empty
​

Transitive property

Blank space 4 empty
​

Converse of Isosceles Triangle Theorem
triangle Q R S is isosceles Definition of isosceles triangle

Answer options with 4 options.

Answer 1

To complete the table demonstrating that triangle QRS is isosceles, we can fill in the blanks with the appropriate moves. Here are the statements that can go in the blanks:

- **Blank space 1:** angle W R S is congruent to angle R S Q
- **Blank space 2:** angle W R T and angle R S Q are corresponding angles
- **Blank space 3:** angle R S Q is congruent to angle R W T
- **Blank space 4:** angle W R S is congruent to angle R Q S

Here’s how the completed table would look:

| Statement | Reason |
|-------------------------------------------------|-------------------------------------|
| line R T is parallel to segment Q S | Given |
| angle W R T is congruent to angle R S Q | Given |
| angle W R S is congruent to angle R S Q | Angles on the same side of the transversal are supplementary (since line RT is parallel) |
| angle W R T and angle R S Q are corresponding angles | Corresponding Angles Theorem |
| angle R S Q is congruent to angle R W T | Transitive property |
| triangle Q R S is isosceles | Converse of Isosceles Triangle Theorem |

Thus, the correct options for the blanks would be filled accordingly.