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2.2: Vertical and Adjacent Angles

Difficulty Level: At Grade Created by: CK-12
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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. AC intersects 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 mAOB, mBOC, mCOD, and mAOD for each of your four locations.

Location 1st 2nd 3rd 4th

What patterns do you notice?

4. If AOD and ______ are vertical angles, then the mAOD ______.

5. If AOB and ______ are vertical angles, then the mAOB ______.

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 AOB and ___________ are adjacent angles formed by two intersecting lines, then the mAOB and ______________ are ______________.

Complete the following problems.

11. Find the value of x and y.

12. Find the value of x.

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