Question

a+ college ready geometry with data analysis u1 l4 angle relationships take note: angle theorems - alternate interior angles ______ if two parallel lines are cut by a transversal, the pairs of alternate interior angles are congruent. - alternate exterior angles ____ if two parallel lines are cut by a transversal, the pairs of alternate exterior angles are congruent. - corresponding angles ____ if two parallel lines are cut by a transversal, the pairs of corresponding angles are congruent. - consecutive (same-side) interior angles theorem ____ if two parallel lines are cut by a transversal, the pairs of consecutive interior angles are supplementary. - consecutive (same-side) exterior angles theorem ______ if two parallel lines are cut by a transversal, the pairs of consecutive exterior angles are supplementary. diagram with angles 1–8

Explanation:

The problem here seems to be about filling in the blanks for the angle theorems (stating the conclusion of each theorem, like "are congruent" or "are supplementary" as per the pattern). Let's analyze each:

Alternate Interior Angles

The theorem says: If two parallel lines are cut by a transversal, the pairs of alternate interior angles are congruent. So the blank should be "are congruent".

Alternate Exterior Angles

The theorem: If two parallel lines are cut by a transversal, the pairs of alternate exterior angles are congruent. So blank: "are congruent".

Corresponding Angles

Theorem: If two parallel lines are cut by a transversal, the pairs of corresponding angles are congruent. Blank: "are congruent".

Consecutive (SAME - SIDE) Interior Angles Theorem

Given: If two parallel lines are cut by a transversal, the pairs of consecutive interior angles are supplementary. So blank: "are supplementary" (but wait, the structure is to state the relationship. Wait, the first part is the name, then the blank. Wait, looking at the format:

For example, Alternate Interior Angles [blank]. Then the statement: If two parallel lines... alternate interior angles are congruent. So the blank for Alternate Interior Angles should be the conclusion, i.e., "are congruent".

Similarly:

• Alternate Exterior Angles: "are congruent"
• Corresponding Angles: "are congruent"
• Consecutive (SAME - SIDE) Interior Angles Theorem: "are supplementary"
• Consecutive (SAME - SIDE) Exterior Angles Theorem: "are supplementary"

Let's list each with their blanks filled:

1. Alternate Interior Angles: are congruent

(Explanation: From the theorem statement, when parallel lines are cut by a transversal, alternate interior angles are congruent.)

1. Alternate Exterior Angles: are congruent

(Explanation: The theorem states that alternate exterior angles formed by parallel lines and a transversal are congruent.)

1. Corresponding Angles: are congruent

(Explanation: Corresponding angles in this scenario (parallel lines, transversal) are congruent.)

1. Consecutive (SAME - SIDE) Interior Angles Theorem: are supplementary

(Explanation: The theorem says consecutive interior angles here are supplementary.)

1. Consecutive (SAME - SIDE) Exterior Angles Theorem: are supplementary

(Explanation: The theorem states consecutive exterior angles in this case are supplementary.)

If we consider the problem as filling these blanks, the answers for each blank (in order) are:

1. are congruent
2. are congruent
3. are congruent
4. are supplementary
5. are supplementary

(Assuming the question is to fill these blanks. If there was a specific angle pair in the diagram (angles 1 - 8) to identify, but since the blanks are for the theorems' conclusions, the above is the filling.)

Answer:

The problem here seems to be about filling in the blanks for the angle theorems (stating the conclusion of each theorem, like "are congruent" or "are supplementary" as per the pattern). Let's analyze each:

Alternate Interior Angles

The theorem says: If two parallel lines are cut by a transversal, the pairs of alternate interior angles are congruent. So the blank should be "are congruent".

Alternate Exterior Angles

The theorem: If two parallel lines are cut by a transversal, the pairs of alternate exterior angles are congruent. So blank: "are congruent".

Corresponding Angles

Theorem: If two parallel lines are cut by a transversal, the pairs of corresponding angles are congruent. Blank: "are congruent".

Consecutive (SAME - SIDE) Interior Angles Theorem

Given: If two parallel lines are cut by a transversal, the pairs of consecutive interior angles are supplementary. So blank: "are supplementary" (but wait, the structure is to state the relationship. Wait, the first part is the name, then the blank. Wait, looking at the format:

For example, Alternate Interior Angles [blank]. Then the statement: If two parallel lines... alternate interior angles are congruent. So the blank for Alternate Interior Angles should be the conclusion, i.e., "are congruent".

Similarly:

• Alternate Exterior Angles: "are congruent"
• Corresponding Angles: "are congruent"
• Consecutive (SAME - SIDE) Interior Angles Theorem: "are supplementary"
• Consecutive (SAME - SIDE) Exterior Angles Theorem: "are supplementary"

Let's list each with their blanks filled:

1. Alternate Interior Angles: are congruent

(Explanation: From the theorem statement, when parallel lines are cut by a transversal, alternate interior angles are congruent.)

1. Alternate Exterior Angles: are congruent

(Explanation: The theorem states that alternate exterior angles formed by parallel lines and a transversal are congruent.)

1. Corresponding Angles: are congruent

(Explanation: Corresponding angles in this scenario (parallel lines, transversal) are congruent.)

1. Consecutive (SAME - SIDE) Interior Angles Theorem: are supplementary

(Explanation: The theorem says consecutive interior angles here are supplementary.)

1. Consecutive (SAME - SIDE) Exterior Angles Theorem: are supplementary

(Explanation: The theorem states consecutive exterior angles in this case are supplementary.)

If we consider the problem as filling these blanks, the answers for each blank (in order) are:

1. are congruent
2. are congruent
3. are congruent
4. are supplementary
5. are supplementary

(Assuming the question is to fill these blanks. If there was a specific angle pair in the diagram (angles 1 - 8) to identify, but since the blanks are for the theorems' conclusions, the above is the filling.)