Introducing Transversals a selfguided lesson Click here to

Introducing Transversals ~ a self-guided lesson ~ Click here to begin

Navigation Instructions On every page in this self-guided lesson, you will need to click a button somewhere to advance or to go back. Shortly after getting started, you will get to a page with a bright green title (“Special Angle Pairs”) and many options to explore. Please be sure to explore every option on that page before clicking the red button to move on. Ready? Get started by clicking the link below! Begin

Introducing Transversals A transversal is a line that passes through two or more lines in the same plane. In each of the three examples above, the red line is a transversal. Next Back

Introducing Transversals Pay careful attention to how many angles are formed when a transversal crosses two lines… 1 2 4 3 5 6 8 7 How many angles do you count in the example above? 1 2 3 4 5 6 7 8 9 There’s more than 1. Try again! There’s more than 2. Try again! There’s more than 3. Try again! There’s more than 4. Try again! There’s more than 5. Try again! There’s more than 6. Try again! There’s more than 7. Try again! Correct! There are 8 angles created by the transversal. There’s fewer than 9. Try again! Next Back

Introducing Transversals Not only does a transversal create a whole bunch of angles when it cuts across two lines, it also creates four different types of special angle pairs. Rather than try to explain what is meant by special angle pairs, it might help to simply introduce you to each kind of pair one by one… Next Back

Introducing Transversals Back Special Angle Pairs Alternate Interior Angles Alternate Exterior Angles There are four types special angle pairs to explore. Take some time to click on each one and get to know them. When you’ve explored them all, click the “Move On” button at the bottom of the page. In each of these mini-lessons, there are interactive problems for you to try. Try your hardest to answer the problems correctly, but don’t worry about a wrong answer here or there! You won’t be assessed until you click “Move On. ” Move On Same-Side Interior Angles Corresponding Angles

Introducing Transversals Alternate Interior Angles Two angles that are on alternate sides of the transversal and lie in the interior space created by the other two lines are called alternate interior angles. Show me the “interior” A good way to remember that this space is the INterior is because it is IN between the two other lines! Show me a pair of Alternate BUTTON Interior COVER 2 Angles There is another pair of alternate interior angles. Can you guess which two angles they are? Angles 3 4 and 5 6 are both on the other pair of interior andinterior lie on alternate sides angles. of the transversal. Find out if you’re right… Type your guess in this box. Next Back to Special Angle Pairs

Introducing Transversals Alternate Interior Angles It is important to be a little more specific about what alternate means with regard to these special angles. In this case, alternate refers to: opposite sides of the transversal AND opposite intersections Back Next Back to Special Angle Pairs

Introducing Transversals Alternate Interior Angles So, keeping our functional definition in mind… “Two angles that are on alternate sides of the transversal and lie in the interior space created by the other two lines. ” …which angle would be an alternate interior angle with angle 3? 1 2 4 5 Try again! This angle is on the exterior. Try again! This angle is on the same intersection as angle 3. Correct! 6 7 8 Try again! This angle is on the same side as angle 3. Try again! This angle is on the exterior. Back Next Back to Special Angle Pairs

Introducing Transversals Alternate Interior Angles “Two angles that are on alternate sides of the transversal and lie in the interior space created by the other two lines. ” Which angle would be an alternate interior angle with angle 2? 1 3 4 5 Try again! This angle is on the same intersection as angle 2. Try again! This angle is on the exterior. 6 Try again! This angle is on the same side as angle 2. 7 8 Correct! Try again! This angle is on the exterior. Back Next Back to Special Angle Pairs

Introducing Transversals Alternate Interior Angles Which of the following pairs are alternate interior angles? 4 and 8 Try again! These angles are on the same side of the transversal. 4 and 7 Correct! 2 and 5 Try again! Both of these angles are on the exterior. 1 and 4 Try again! These angles are on the same intersection. Back Next Back to Special Angle Pairs

Introducing Transversals Alternate Interior Angles Which of the following pairs are alternate interior angles? 3 and 8 Correct! 5 and 7 Try again! Angle 5 is actually on the exterior. 3 and 7 Try again! Both of these angles are on the same side of the transversal. 2 and 5 Try again! These angles are both on the exterior. Back Next Back to Special Angle Pairs

Introducing Transversals Alternate Interior Angles Which of the following pairs are alternate interior angles? *CHALLENGE* 8 and 9 Try again! These angles are on the same side of the transversal. 6 and 9 Try again! Angle 6 is actually on the exterior. 4 and 9 Try again! Angle 4 is actually on the exterior. 7 and 9 Correct! This is the end of the mini-lesson on Alternate Interior Angles. Back to Special Angle Pairs Back

Introducing Transversals Same-Side Interior Angles Two angles that are on the same-side of the transversal and lie in the interior space created by the other two lines are called same-side interior angles. Show me the “interior” A good way to remember that this space is the INterior is because it is IN between the two other lines! Show me a pair of Same-Side Interior BUTTON COVER 2 Angles There is another pair of same-side interior angles. Can you guess which two angles they are? Angles 3 and 6 are Angles 4 and 5 are both on the other pair of interior and lie on same-side interior the same side of angles. the transversal. Find out if you’re right… Type your guess in this box. Next Back to Special Angle Pairs

Introducing Transversals Same-Side Interior Angles It is important to be a little more specific about what same-side means with regard to these special angles. In this case, same-side refers to: the same side of the transversal Back Next Back to Special Angle Pairs

Introducing Transversals Same-Side Interior Angles So, keeping our functional definition in mind… “Two angles that are on the same-side of the transversal and lie in the interior space created by the other two lines. ” …which angle would be an same-side interior angle with angle 3? 1 2 Try again! This angle is on the exterior. 4 5 Try again! This angle is on the opposite side of the transversal as angle 3. 6 7 8 Correct! Try again! This angle is on the exterior. Back Next Back to Special Angle Pairs

Introducing Transversals Same-Side Interior Angles “Two angles that are on the same-side of the transversal and lie in the interior space created by the other two lines. ” Which angle would be an same-side interior angle with angle 1? 2 3 4 5 Try again! This angle is on the opposite side of the transversal as angle 1. Try again! This angle is on the exterior. Correct! 6 7 Try again! This angle is on the exterior. 8 Try again! This angle is on the opposite side of the transversal as angle 1. Back Next Back to Special Angle Pairs

Introducing Transversals Same-Side Interior Angles Which of the following pairs are same-side interior angles? 1 and 4 Try again! These two angles are not on the same side of the transversal. 7 and 8 Try again! These two angles are not on the same side of the transversal. 1 and 7 Correct! 5 and 6 Try again! These angles are on the exterior. Back Next Back to Special Angle Pairs

Introducing Transversals Same-Side Interior Angles Which of the following pairs are Same-Side interior angles? *CHALLENGE* 2 and 11 2 and 10 Try again! These angles are on the opposite sides of the transversal. Correct! 3 and 5 Try again! This answer is really tricky…. Believe it or not, in this answer, angle 5 is considered to be on the exterior. 7 and 10 Try again! This answer is really tricky…. Believe it or not, in this answer, angle 7 is considered to be on the exterior. This is the end of the mini-lesson on Same-Side Interior Angles. Back to Special Angle Pairs Back

Introducing Transversals Alternate Exterior Angles Two angles that are on alternate sides of the transversal and lie in the exterior space created by the other two lines are called alternate exterior angles. Show me the “exterior” The exterior space is OUTSIDE of the two other lines. Show me a pair of Alternate BUTTON Exterior COVER 2 Angles There is another pair of alternate exterior angles. Can you guess which two angles they are? Angles 2 and 8 are 1 and 7 are Angles the other pair of on the both alternate exterior and lie on angles. alternate sides of the transversal. Find out if you’re right… Type your guess in this box. Next Back to Special Angle Pairs

Introducing Transversals Alternate Exterior Angles It is important to be a little more specific about what alternate means with regard to these special angles. In this case, alternate refers to: opposite sides of the transversal AND opposite intersections Back Next Back to Special Angle Pairs

Introducing Transversals Alternate Exterior Angles So, keeping our functional definition in mind… “Two angles that are on alternate sides of the transversal and lie in the exterior space created by the other two lines. ” …which angle would be an alternate exterior angle with angle 1? 2 Try again! This angle is on the same intersection as angle 1. 3 4 5 Try again! This angle is on the interior. 6 7 Try again! This angle is on the interior. Correct! 8 Try again! This angle is on the same side of the transversal as angle 1. Back Next Back to Special Angle Pairs

Introducing Transversals Alternate Exterior Angles “Two angles that are on alternate sides of the transversal and lie in the exterior space created by the other two lines. ” Which angle would be an alternate exterior angle with angle 4? 1 2 3 5 Try again! This angle is on the same intersection as angle 1. Try again! This angle is on the interior. 6 7 8 Correct! Try again! This angle is on the same side as angle 1. Try again! This angle is on the interior. Back Next Back to Special Angle Pairs

Introducing Transversals Alternate Exterior Angles Which of the following pairs are alternate exterior angles? 3 and 5 Try again! These angles are on the same side of the transversal. 2 and 5 Correct! 2 and 6 Try again! These angles are on the same side of the transversal. 1 and 5 Try again! Angle 1 is actually on the interior. Back Next Back to Special Angle Pairs

Introducing Transversals Alternate Exterior Angles Which of the following pairs are alternate exterior angles? 3 and 8 Try again! Angle 8 is actually on the interior. 4 and 7 Try again! Both of these angles are on the same side of the transversal. 3 and 5 Try again! Angle 5 is actually on the interior. 3 and 7 Correct! Back Next Back to Special Angle Pairs

Introducing Transversals Alternate Exterior Angles Which of the following pairs are alternate exterior angles? *CHALLENGE* 2 and 10 Try again! These angles are on the same side of the transversal. 2 and 7 Try again! These angles are on the same side of the transversal. 2 and 6 Correct! 6 and 10 Try again! Believe it or not, angle 6 actually lies on the interior in this problem. This is the end of the mini-lesson on Alternate Exterior Angles. Back to Special Angle Pairs Back

Introducing Transversals Corresponding Angles Two angles that lie in the same corresponding location at different intersections along the transversal are called corresponding angles. Show me a pair of Corresponding Angles In the diagram at the right, angles 1 and 5 are in the same corresponding corner of their respective intersections. That’s what makes them corresponding angles. Now that one pair has identified for you, how many additional pairs of corresponding angles are there? 21 5 6 3 4 21 3 45 6 5231 4 Sorry, in addition to the pair Sorry, in to Correct! There that was identified earlier, there that are three additional are corresponding angle pairs. corresponding angle corresponding pairs. Each pair of of corresponding angles is is color coded in in the diagram above. diagram 65 Next Back to Special Angle Pairs

Introducing Transversals Corresponding Angles Sometimes it helps to actually describe the location of each angle to make sure they correspond to one another. For example, angle 2 is in the “top right” corner of it’s intersection. Which other angle is also sitting at the “top right” corner of it’s intersection? 1 3 4 5 Try again! This angle in on the same intersection as angle 2. Try again! This angle is on the top left corner of its intersection. 6 7 8 Correct! Try again! This angle is on the bottom right corner of its intersection. Try again! This angle is on the bottom left corner of its intersection. Back Next Back to Special Angle Pairs

Introducing Transversals Corresponding Angles So, keeping our functional definition in mind… “Two angles that lie in the same corresponding location at different intersections along the transversal. ” …which angle would be an corresponding angle with angle 3? 1 Try again! This angle is on the same intersection as angle 3. 2 4 5 Try again! This angle is on the same intersection as angle 3. Try again! This angle is in a bottom left corner. Is angle 3 in a bottom left corner? 6 Correct! 7 8 Try again! This angle is in a top right corner. Is angle 3 in a top right corner? Try again! This angle is in a top left corner. Is angle 3 in a top left corner? Back Next Back to Special Angle Pairs

Introducing Transversals Corresponding Angles “Two angles that lie in the same corresponding location at different intersections along the transversal. ” Which angle would be an corresponding angle with angle 8? 1 2 3 4 Try again! This angle is in a top right corner. Is angle 8 in a top right corner? Correct! Try again! This angle is in a bottom left corner. Is angle 8 in a bottom left corner? Try again! This angle is in a top left corner. Is angle 8 in a top left corner? 5 6 7 Try again! This angle is on the same intersection as angle 8. Back Next Back to Special Angle Pairs

Introducing Transversals Corresponding Angles Which of the following pairs are corresponding angles? 3 and 8 Try again! Angle 3 is to the right of its intersection, angle 8 is to the left of its intersection. 2 and 5 Try again! Angle 2 is above its intersection, angle 5 is below its intersection. 4 and 5 Correct! 3 and 5 Try again! Angle 3 is to the right of its intersection, angle 5 is below its intersection. Back Next Back to Special Angle Pairs

Introducing Transversals Corresponding Angles Which of the following pairs are NOT corresponding angles? 3 and 8 Try again! These are both in the bottom left corner of their respective intersections. 2 and 7 Try again! These are both in the bottom left corner of their respective intersections. 4 and 6 Correct! None of the above Try again! One of these answers is not a pair of corresponding angles. . . Back Next Back to Special Angle Pairs

Introducing Transversals Corresponding Angles Which of the following pairs are corresponding angles? *CHALLENGE* 3 and 12 Correct! 5 and 12 Try again! Angle 5 is in the bottom right corner, angle 12 is in the top right corner. 4 and 12 Try again! Angle 4 is in the bottom left corner, angle 12 is in the top right corner. 4 and 10 Try again! This one is tricky… Angle 4 is in the bottom left corner, angle 10 is in the top left corner. This is the end of the mini-lesson on Corresponding Angles. Back to Special Angle Pairs Back

Introducing Transversals Checkpoint Have you taken the time to get comfortable with all four of the special angle pairs? Can you describe in your own words how to identify: • • Alternate Interior Angles? Alternate Exterior Angles? Same-Side Interior Angles? Corresponding Angles? Could you point to examples of each on the diagram at the right? If you can, go ahead and take the Review Assessment. If not, go back and take another look at each of the different special angle pair mini-lessons. Note: once you go on to the Review Assessment, you cannot go back. Take the Review Assessment Back to Special Angle Pairs

Introducing Transversals Review Assessment Question 1 What kind of angle pair are angles 4 and 7? Alternate Interior Angles Incorrect. The correct answer is Alternate Exterior Angles Correct! Same-Side Interior Angles Incorrect. The correct answer is Alternate Exterior Angles. Corresponding Angles Incorrect. The correct answer is Alternate Exterior Angles. Next Question

Introducing Transversals Review Assessment Question 2 Which of the following pairs are corresponding angles? 3 and 7 Incorrect. The correct answer is 1 and 7. 1 and 5 Incorrect. The correct answer is 1 and 7. 3 and 6 Incorrect. The correct answer is 1 and 7 Correct! Next Question

Introducing Transversals Review Assessment Question 3 Which angle would form a pair of alternate interior angles with angle 6? 1 Incorrect. The correct answer is 2. 2 Correct! 4 Incorrect. The correct answer is 2. 5 Incorrect. The correct answer is 2. Next Question

Introducing Transversals Review Assessment Question 4 Which of the following angle pairs are same-side interior angles? 2 and 11 Correct! 2 and 5 Incorrect. The correct answer is 2 and 11. This was tricky. . . But if you ignore angles 9 -12, you’ll see that angle 5 is an exterior angle. 3 and 11 Incorrect. The correct answer is 2 and 11. These two angles are actually alternate interior angles. 7 and 11 Incorrect. The correct answer is 2 and 11. This was tricky. . . But if you ignore angles 1 -4, you’ll see that angle 6 is an exterior angle. Next Question

Introducing Transversals Review Assessment Question 5 What kind of angle pair are angles 3 and 12? Alternate Interior Angles Incorrect. The correct answer is Corresponding Angles. Alternate Exterior Angles Incorrect. The correct answer is Corresponding Angles. Same-Side Interior Angles Incorrect. The correct answer is Corresponding Angles Correct! Next Page Question

This completes the learning module. You may now begin the assignment from the textbook: