2.2: Vertical and Adjacent Angles
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. intersects at point .
Name two pairs of vertical angles.
3. Move point or point to four different locations where the angles have different measures. Record , , , and for each of your four locations.
Location | ||||
---|---|---|---|---|
What patterns do you notice?
4. If and ______ are vertical angles, then the ______.
5. If and ______ are vertical angles, then the ______.
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 or point and make a conjecture about adjacent angles formed by two intersecting lines. Hint: You may have to do a calculation.
10. If and ___________ are adjacent angles formed by two intersecting lines, then the and ______________ are ______________.
Complete the following problems.
11. Find the value of and .
12. Find the value of .