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SECTION 2.4 Vertical Angles

In this lesson, students will explore the Vertical Angles Theorem and the Linear Pair Postulate. They will learn to identify vertical angles, which are not adjacent and formed by two intersecting lines, as well as linear pairs, which consist of two adjacent angles whose non-common sides lie on the same line. Through hands-on activities like using a straightedge and protractor, students will solve problems to find angle measures and understand the relationships between angles formed by intersecting lines.

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SECTION 2.4 Vertical Angles

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  1. SECTION 2.4Vertical Angles LEARNING TARGETS: 1. Students will be able to use and apply the Vertical Angles Theorem. 2. Students will be able to use and apply the Linear Pair Postulate. VOCABULARY Vertical Angles and Linear Pair

  2. Question: • What is the relationship between the angles formed by two intersecting lines. • Materials: • Paper • Straightedge • Protractor Page 74

  3. STEP 1:

  4. STEP 2:

  5. STEP 3:

  6. THINK ABOUT IT

  7. VOCABULARY: Which of the above angles are vertical? • Vertical Angles: • Two angles that are not adjacent and whose sides are formed by two intersecting lines.

  8. VOCABULARY: Which of the above angles are linear pairs? • Linear Pair: • Two adjacent angles who non-common sides are on the same line.

  9. Example (Notes)

  10. Example (Textbook)

  11. Postulate 7: • Linear Pair Postulate • If two angles form a linear pair, then they are supplementary.

  12. Example (Notes) Find the measure of ∠RSU. Find the measures of ∠HJK and ∠KJN.

  13. Theorem 2.3: • Vertical Angles Theorem

  14. PROOF OF THEOREM:

  15. Example (Textbook)

  16. Example (Notes) Find m∠1, m∠2, and m∠3.

  17. Example (Notes) Find the value of x.

  18. Example (Notes) Find the value of x.

  19. Example (Notes) Find the value of x.

  20. DAILY PUZZLER: When two lines intersect, the measure of one of the angles they form is 20° less than three times the measure of one of the other angles formed. What are the measures of all four angles formed by the two lines?

  21. Cooperative Learning: • Vertical Angles Worksheet

  22. HOMEWORK: • Section 2.4 Assignment • Page 78 #10-50 EVEN, 51-56 ALL • Due Tuesday, 10/25

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