Lesson 2.1 Perpendicularity Complements & Supplements Lesson 2.2.

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Presentation transcript:

Lesson 2.1 Perpendicularity Complements & Supplements Lesson 2.2

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

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

A C D B Given: AB BC DC BC Conclusion: <B = <C ~ Τ Τ StatementReasons 1.AB BC 2.<B is a right <. 3.DC BC 4.<C is a right <. 5. <B = <C Τ 1.Given 2.If 2 segments are, they form a right <. 3.Given. 4.If 2 segments are, they form a right <. 5.If <‘s are right <‘s, they are =. Τ Τ Τ ~ ~

Given: KJ KM <JKO is 4 times as large as <MKO Find: m<JKO Τ M J K O x° 4x° 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

Given: EC ll x axis CT ll y axis Find the area of RECT x axis y axis C (7, 3) T R (-4,-2) E 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.

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

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

Supplementary Angles  Supplementary angles are two angles whose sum is 180° (a straight angle).  Each of the two angles is called the supplement of the other. J K130° 50° <J & <K are supplementary.

Given: Diagram as shown Conclusion: <1 is supplementary to <2 ABC 12 StatementReasons 1.Diagram as shown. 2.<ABC is a straight angle. 3.<1 is supplementary to <2. 1.Given 2.Assumed from diagram 3.If the sum of two <‘s is a straight <, they are supplementary.