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2.2: Vertical and Adjacent Angles

Created by: CK-12

This activity is intended to supplement Geometry, Chapter 1, Lesson 5.

Problem 1 – Exploring Vertical Angles

1. Define Vertical (or Opposite) Angles.

2. Open the Cabri Jr. file VERTICAL. \overleftrightarrow{AC} intersects \overleftrightarrow{BD} at point O.

Name two pairs of vertical angles.

3. Move point B or point C to four different locations where the angles have different measures. Record m\angle{AOB}, m\angle{BOC}, m \angle{COD}, and m\angle{AOD} for each of your four locations.

Location 1^{st} 2^{nd} 3^{rd} 4^{th}

What patterns do you notice?

4. If \angle{AOD} and ______ are vertical angles, then the m\angle{AOD} ______.

5. If \angle{AOB} and ______ are vertical angles, then the m\angle{AOB} ______.

6. Based on your data from Question 3, make a conjecture about vertical angles in general.

Problem 2 – Exploring Adjacent Angles

7. Define Adjacent Angles.

8. Use the file VERTICAL from Problem 1. Identify all four pair of adjacent angles.

9. Move point B or point C and make a conjecture about adjacent angles formed by two intersecting lines. Hint: You may have to do a calculation.

10. If \angle{AOB} and ___________ are adjacent angles formed by two intersecting lines, then the m\angle{AOB} and ______________ are ______________.

Complete the following problems.

11. Find the value of x and y.

12. Find the value of x.

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