1. Year 2 Warm Up For #1-2 find the rule, then find the next three terms in the sequence. 1. 2,-4,-10, -16, -22… 2. -8, -4, 0, 4, 8… 3. Find the slope of (-8, 7) and (-8, 6) 4. Find the slope of (-2, 7) and (-8, 7) 1. -6; -28,-34,-40 2. 4; 12,16,20 3. undefined 4. m=0

2. 2.5 Angle Relationships  Investigation 1 “The Linear Pair Conjecture”  Step 1) Draw PQ with point R between points P and Q.  Step 2) Draw RS – Now you have a Linear Pair  Step 3) Label the angles <1 and <2.  Step 4) Use your protractor to measure <1 and <2.  Step 5) Compare your results for your two angles’ measures with your group or a classmate.  What do you notice about the two angles? Linear Pair Conjecture

3. Angle Relationships  Linear Pair Conjecture – If two angles form a linear pair, then the measures of the angles add up to 180 degrees. 12 <1+<2=180 °

4. Angle Relationships  Investigation 2 “Vertical Angles Conjecture”  Step 1) Draw two intersecting lines that are not perpendicular onto patty paper. Label the angles as shown:  Which angles are vertical?  Step 2) Fold the patty paper so that one pair of vertical angles lie over each other. Vertical Angles Conjecture 1 2 3 4

5.  What do you notice about their measure?  Vertical Angles Conjecture: If two angles are vertical angles, then they are congruent. 1 2 3 4 <1=<3<2=<4

6. Find the missing measures  Ex 1) ab c 130° a = b = c = 50° 130° 50°

7. Find the missing measures  Ex 2) a c 65° b a = b = c = 90° 25° 90°

8. Find the missing measures  Ex 3) b c 30° d 50° a a = b = c = d = 30° 100° 50° 100°

9. Algebra with Angles – Ex 1 a) State the type of angles b) State the relationship c) Solve for x. d) Then find measure of each angle. m<1 = 3x-40 2x-10 = m<2

10. Answer 1 The angles are vertical, therefore they are congruent. This means that the measures of each angle are equal. m<1 = m<2 3x-40 = 2x – 10 x – 40 = -10 x = 30 Step 1: Set up the angle relationship. Step 2: Substitute in values. Step 3: Solve for x. Step 4: Plug back in to find angle measures. m<1 = 50° m<2 = 50° m<1 = 3(30) - 40 m<2 = 2(30) - 10

11. Algebra with Angles – Ex 2 a) State the type of angles b) State the relationship c) Solve for x d) Find the measure of angle 1. m<1 = 4x - 20 m<2 =x

12. Answer – Ex. 2 <1 and <2 form a line making them a linear pair which adds up to 180 degrees. Therefore, m<1 +<2 = 180° (4x – 20) + (x) = 180 5x – 20 = 180 5x = 200 x = 40° m<2 = 40°, m<1 = 140° Step 1: Set up the angle relationship. Step 2: Substitute in values. Step 3: Solve for x. Step 4: Plug back in to find angle measures.

13. Summary : Make a chart below showing the angle types(vertical, linear pair, and right angles), their relationships(congruent, supplementary, complementary), and a sketch for each.

14. Homework  Homework 2.5 worksheet Classwork 2.5 Worksheet and Bookwork p. 122 #1-6…you must copy the pictures and show your work!!! In Class Practice