Math Problem Statement

Which angles are alternate interior angles?

Solution

In the diagram, EG\overleftrightarrow{EG} and HJ\overleftrightarrow{HJ} are parallel lines, and the question asks for alternate interior angles. Alternate interior angles occur when two parallel lines are crossed by a transversal, and they lie on opposite sides of the transversal but inside the parallel lines.

Here, HI\overleftrightarrow{HI} acts as the transversal between the parallel lines EG\overleftrightarrow{EG} and HJ\overleftrightarrow{HJ}.

The correct pair of alternate interior angles are:

  • HIF\angle HIF (on the lower side of the transversal)
  • EFD\angle EFD (on the upper side of the transversal).

So the correct answer is:

HIF and EFD\boxed{\angle HIF \text{ and } \angle EFD}

Would you like more details or have any other questions?

Here are five related questions for further practice:

  1. What are corresponding angles in this diagram?
  2. How do you prove that alternate interior angles are equal when lines are parallel?
  3. Which angles are supplementary in this diagram?
  4. What is the relationship between HIF\angle HIF and GFI\angle GFI?
  5. Can FD\overleftrightarrow{FD} and HI\overleftrightarrow{HI} be considered parallel?

Tip: Always look for the transversal when identifying alternate interior angles between parallel lines.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Parallel Lines
Transversals
Alternate Interior Angles

Formulas

-

Theorems

Alternate Interior Angles Theorem

Suitable Grade Level

Grades 6-8