<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
Dismiss
Skip Navigation

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. \begin{align*}\overleftrightarrow{AC}\end{align*}AC intersects \begin{align*}\overleftrightarrow{BD}\end{align*}BD at point \begin{align*}O\end{align*}O.

Name two pairs of vertical angles.

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

Location \begin{align*}1^{st}\end{align*}1st \begin{align*}2^{nd}\end{align*}2nd \begin{align*}3^{rd}\end{align*}3rd \begin{align*}4^{th}\end{align*}4th
\begin{align*}m\angle{AOB}\end{align*}mAOB
\begin{align*}m\angle{BOC}\end{align*}mBOC
\begin{align*}m\angle{COD}\end{align*}mCOD
\begin{align*}m\angle{AOD}\end{align*}mAOD

What patterns do you notice?

4. If \begin{align*}\angle{AOD}\end{align*}AOD and ______ are vertical angles, then the \begin{align*}m\angle{AOD}\end{align*}mAOD ______.

5. If \begin{align*}\angle{AOB}\end{align*}AOB and ______ are vertical angles, then the \begin{align*}m\angle{AOB}\end{align*}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 \begin{align*}B\end{align*}B or point \begin{align*}C\end{align*}C and make a conjecture about adjacent angles formed by two intersecting lines. Hint: You may have to do a calculation.

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

Complete the following problems.

11. Find the value of \begin{align*}x\end{align*}x and \begin{align*}y\end{align*}y.

12. Find the value of \begin{align*}x\end{align*}x.

Image Attributions

Show Hide Details
Files can only be attached to the latest version of section
Reviews
Help us create better content by rating and reviewing this modality.
Loading reviews...
Please wait...
Please wait...
Image Detail
Sizes: Medium | Original
 
TI.MAT.ENG.SE.1.Geometry.2.2