Question

Given: a and b are parallel and c is a transversal. Prove: ∠2 ≅ ∠7 Use the drop-down menus to complete the paragraph proof showing that alternate interior angles are congruent. We know that lines a and b are parallel and that line c is a transversal because that is given. We can tell that angles 2 and 5 are congruent because "blank" angles are congruent. Angles 5 and 7 are congruent because "blank" angles by parallel lines cut by a transversal are congruent. Therefore, angles 2 and 7 are congruent based on the "blank"

here are then answers to chose from the following segment.
 1st, vertical, corresponding,  alternate interior, alternate exterior

2ent, vertical, corresponding,  alternate interior, alternate exterior

3erd, symmetric  property, definition of substance, transitive property, corresponding angles 
postulate

Answer 1

First blank: vertical
Second blank: corresponding
Third blank: transitive property

Hope this helps :)

Answer 2

Part 1) Vertical angles

Part 2) Corresponding angles

Part 3) Transitive property

Explanation:

Part 1) We can tell that angles
`2` and
`5` are congruent because

`m<2=m<5` ------> by vertical angles

so

Angles
`2` and
`5` are congruent

Part 2) Angles 5 and 7 are congruent because

`m<5=m<7` ------> by corresponding angles

so

Angles
`5` and
`7` are congruent

Part 3) Angles
`2` and
`7` are congruent based on

we know that

The Transitive Property of Equality. states that

If
`a = b` and
`b = c`,

then

`a = c`

In this part we have

`m<2=m<5`

`m<5=m<7`

therefore

`m<2=m<7` -----> by transitive property