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# 2.2: Vertical and Adjacent Angles

Difficulty Level: At Grade 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 $1^{st}$ $2^{nd}$ $3^{rd}$ $4^{th}$
$m\angle{AOB}$
$m\angle{BOC}$
$m\angle{COD}$
$m\angle{AOD}$

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

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 $x$.

Feb 23, 2012

Nov 03, 2014