* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download angle
Survey
Document related concepts
Technical drawing wikipedia , lookup
Perspective (graphical) wikipedia , lookup
Cartesian coordinate system wikipedia , lookup
Rotation formalisms in three dimensions wikipedia , lookup
Pythagorean theorem wikipedia , lookup
Integer triangle wikipedia , lookup
Perceived visual angle wikipedia , lookup
History of trigonometry wikipedia , lookup
Line (geometry) wikipedia , lookup
Rational trigonometry wikipedia , lookup
Multilateration wikipedia , lookup
Trigonometric functions wikipedia , lookup
Transcript
1.6 Angle Relationships 9/10/12 • Pairs of Angles – Adjacent Angles – Vertical Angles – Linear Pair – Complementary – Supplementary CCSS: G-CO1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. Mathematical Practice 1. Make sense of problems, and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments, and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for, and make use of, structure. 8. Look for, and express regularity in, repeated reasoning. E.Q: • 1. What are characteristics of complementary, supplementary, adjacent, linear and vertical angles? • 2. How do we use the formulas for area and perimeter of 2-D shapes to solve real life situations? Adjacent Angles • Adjacent angles – two angles that lie in the same plane, have a common vertex, and share a common side, but NO common interior points. C A C B A B D ABC and CBD D Vertical Angles • Vertical angles – two nonadjacent angles formed by two intersecting lines. B A E C D AEBand CED AEDand BEC Linear Pair • A linear pair – a pair of adjacent angles whose non-common sides are opposite rays. B D E C BEDand BEC Identify Angle Pairs • Name an angle pair that satisfies each condition. a. Two obtuse vertical angles. VZXand YZW b. Two acute adjacent angles. VZYand YZT YZTandTZW TZWand WZX X V 115° Z 65° 65° 50° 65° Y T W Angle Relationships • Complementary Angles – Two angles whose measures have a sum of 90°. A B E 50° 40° 1 2 D C 1and 2 ABCand DEF F Angle Relationships • Supplementary Angles – Two angles whose measures have a sum of 180°. A C D 80° M B N 100° M and N ABDand CBD Angle Measures • Find the measure of two complementary angles if the difference of the measures is 12. x° A B Angle Measures • Find the measure of two complementary angles if the difference of the measures is 12. mB mA 12 (90 x) x 12 90 2x 12 2x 78 x 39 mA 39 mB 90 39 51 Perpendicular Lines • Perpendicular lines – lines that form right angles – Intersect to form four right angles. – Intersect to form congruent adjacent angles. – Segments and rays can be perpendicular to lines or to the other line segments and rays. – The right angle symbol in the figure indicates that the lines are perpendicular. Y • • XZ is read “is perpendicular to”. WY X Z W Perpendicular Lines • Find x and y so that BE and AD are perpendicular. mBFD mBFC CFD 90 6 x 3x B 90 9x 10 x 6x° 3x° A mAFE 12 y 10 90 12 y 10 100 12 y 25 y 3 C (12y – 10)° F E D 1.7 Introduction to Perimeter, Circumference, & Area 9/10/12 Rectangle W (width) • Perimeter P=2l +2w l (length) • Area A=lw Square • Perimeter P=4s S (side) • Area A=s2 Example: Find the perim. & area of the figure. • P=2l +2w 5 in P=2(5in)+2(3in) P=10in+6in P=16in 3 in • A=lw A=(5in)(3in) A=15in2 Ex: Find the perim. & area of the figure. • P=4s P=4(20m) P=80m 20 m • A=s2 A=(20m)2 A=400m2 Triangle • Perimeter P=a+b+c a c h (height) b • Area A= ½ bh (base) Ex: Find the perim. & area of the figure. • P=a+b+c P=5ft+7ft+6ft P=18 ft 5 ft 4 ft 7 ft 6 ft • A= ½ bh A= ½ (7ft)(4ft) A= ½ (28ft2) A= 14ft2 Circle • Diameter d=2r • Circumference C=2πr • Area A=πr2 diameter ** Always use the π button on the calculator; even when the directions say to use 3.14. Ex: Find the circumference & area of the circle. • C=2πr C=2π(5in) C=10π in C≈31.4 in • A=πr2 A=π(5in)2 A=25π in2 A≈78.5 in2 GROUP WORK CHAMPs #2