Question

Kassidy wants to prove that the interior angles of any triangle sum to 180°. She draws a line through one vertex parallel to the opposite side, and then she labels all the angles formed.

Drag a reason to match each statement in Kassidy's two-column proof in the table below.

Answer 1

1.A straight line measures 180 degrees

2.Alternate interior angles theorem

Explanation:

We have to prove that

Sum of interior angles of any triangle =180 degrees

Proof:

1.
`m\angle 1+m\angle 4+m\angle 5=180^(\circ)`

Reason: A straight line measures 180 degrees

2.
`\angle 4\cong\angle 2`

`\angle 5\cong \angle 3`

Reason:Alternate interior angles theorem

3.
`m\angle 4=m\angle 2,m\angle 3=m\angle 5`

Reason: by definition of congruent angles.

4.
`m\angle 1+m\angle 1+m\angle 3=180^(\circ)`

Reason: By substitution

Hence, proved.

Answer 2

First box: A straight line measures 180 degrees

Second box: Alternate interior angles theorem

Explanation:

All lines are straight, and therefore measure 180 degrees

You can see that the red line is parallel to the line with angles 2 and 3. Alternate interior angles are two interior angles which lie on different parallel lines and on opposite sides of a transversal. Which justifies step 2