1. Lesson 2.1 Complements & Supplements Perpendicularity Lesson 2.2

2. Perpendicular: lines, rays or segments that intersect at right angles. Symbol for perpendicular Τ X B b A B a A D Y AB Τ BD a Τ b XY Τ AB

3. If <B is a right angle, then AB BC Τ A C B Can’t assume unless you have a right angle or given. Τ

4. A D Given: AB BC DC BC Conclusion: <B = <C Τ Τ ~ C B Statement Reasons • AB BC • <B is a right <. • DC BC • <C is a right <. • <B = <C Τ • Given • If 2 segments are , they form a right <. • Given. • If 2 segments are , they form a right <. • If <‘s are right <‘s, they are =. Τ Τ Τ ~ ~

5. J Given: KJ KM <JKO is 4 times as large as <MKO Find: m<JKO Τ O 4x° x° M K Solution: Since KJ KM, m<JKO + m<MKO = 90°. 4x + x = 90 5x = 90 x = 18 Substitute 18 for x, we find that m<JKO = 72°. Τ

6. y axis Given: EC ll x axis CT ll y axis Find the area of RECT C (7, 3) E 321 123 x axis -3 -2 -1 1 2 3 R (-4,-2) T Solution: The remaining coordinates are T = (7, -2) and E = (-4, 3). So RT = 11 and TC = 5 as shown. Area = base times height. A = bh = (11)(5) =55 The area of RECT is 55 square units.

7. Complementary Angles 40° A B 50° <A & <B are complementary. Complementary angles are two angles whose sum is 90°. Each of the two angles is called the complement of the other.

8. More Complementary Angles C 60° J F 63°40’ 30° 26°20’ D E G H <FGJ is the complement of <JGH. <C is complementary to <E.

9. Supplementary Angles 130° K 50° J <J & <K are supplementary. Supplementary angles are two angles whose sum is 180° (a straight angle). Each of the two angles is called the supplement of the other.

10. 1 2 A B C Statement Reasons • Diagram as shown. • <ABC is a straight angle. • <1 is supplementary to <2. • Given • Assumed from diagram • If the sum of two <‘s is a straight <, they are supplementary. Given: Diagram as shown Conclusion: <1 is supplementary to <2