1. Midterm Review Project: Angle Pairs BY: [NAME REMOVED]

2. Angle Pairs: Definitions Parallel Lines: A pair of lines that never cross Vertical Angles: A pair of angles that are vertical to each other, and are congruent Transversal: A line that crosses a set of parallel lines Linear Pair Angles: Two angles that are next to each other on a line, and are supplementary B C B C

3. Definitions Alternate Exterior Angles: Lines that are opposite of each other, on the outside of parallel lines, and are congruent Consecutive Exterior Angles: Two angles, on one side of a transversal, and on the inside of two parallel lines Alternate Interior Angles: Two opposite angles on the interior of parallel lines, and are congruent Corresponding Angles: The angles in matching corners of where the transversal intersects two parallel lines B C B C B C B C

4. Postulates and Theorems Linear Pairs Postulate- A linear pair will always add to 180 degrees Vertical Pairs Postulate- Vertical pairs are always congruent Corresponding Angles Theorem- Corresponding angles are always congruent Alternate Exterior Angles Theorem- Alternate exterior angles are always congruent Alternate Interior Angles Theorem- Alternate interior angles are always congruent Consecutive Interior Angles Theorem- A pair of consecutive interior angles will always be supplementary

5. Tips and Tricks While working on these problems, remember that if it’s too hard for you to remember all these theorems and postulates, then just try to remember these three: the vertical angles postulate, linear pairs postulate, and the alternate interior angles theorem. For any angles pair problem you can use these three to find the answer. For example, in the problem below you want to know the measure of angle A. You know that C=36 because of the Vertical Pairs postulate. Then, you know that C=B because of the Alternate Interior Angles theorem, and finally, you know that A=144 because you know that B=36 so, because of the Linear Pairs Postulate, 180-36=144. A 36 B C And Don’t Forget to Read the Question!! Use your toolbox!!

6. Example 1 Find the measure of angles a and b. Use the vertical angles theorem to find that a=88 Use the Alternate Interior angles theorem to find that b=92. a=88 Vertical Angles Theorem b=92 Alternate Interior Angles Theorem 92 88b a

7. Example 2 Find the measure of angles a, b, and c. Use the Corresponding Angles Theorem to find that a=102 Next, use the Corresponding Angles Theorem to find that b=93 Finally, use the Linear Pairs Postulate to find that c=87 b c93 102 a 180 -93 87 a=102 b=93 c=87

8. Problem #1 Find the measures of angles a and g. g a 68

9. Problem #2 Find the measures of angles c and u. (Think of x as an unknown value) x 23 u c

10. Problem #3 Find the measures of angles p and b. p b X-6 62-x

11. Problem #4 Find the value of angles h and e. h 65 e 32

12. Problem #5 Find the measures of angles h, s, and o. 97 y-29 y+47 O S 42 90 B

13. Answer Key Problem 1:Problem 3: Problem 5: a=112p=151 h=97 g=112 b=29 s=97 o=128 Problem 2: Problem 4: c=67h=57 u=157 e=122