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. A B C D A B C D
Vertical Angles Vertical angles – two nonadjacent angles formed by two intersecting lines. A B D C E
Linear Pair A linear pair – a pair of adjacent angles whose non-common sides are opposite rays. B D CE
Identify Angle Pairs Name an angle pair that satisfies each condition. a.Two obtuse vertical angles. b.Two acute adjacent angles. Y T W V Z X 115° 65° 50°
Angle Relationships Complementary Angles –Two angles whose measures have a sum of 90°. 1 2 A C B DF 50° E 40°
Angle Relationships Supplementary Angles –Two angles whose measures have a sum of 180°. A D BC M N 80° 100°
Angle Measures Find the measure of two complementary angles if the difference of the measures is 12. A B x°x°
Angle Measures Find the measure of two complementary angles if the difference of the measures is 12.
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. is read “is perpendicular to”. XZ WY XZ Y W
Perpendicular Lines Find x and y so that BE and AD are perpendicular. AD B E F C 6x° 3x° (12y – 10)°
1.7 Introduction to Perimeter, Circumference, & Area 9/10/12
Rectangle Perimeter P=2 l +2 w Area A= lw l (length) W (width)
Square Perimeter P=4s Area A=s 2 S (side)
Example: Find the perim. & area of the figure. P=2 l +2 w P=2(5in)+2(3in) P=10in+6in P=16in A= lw A=(5in)(3in) A=15in 2 3 in 5 in
Ex: Find the perim. & area of the figure. P=4s P=4(20m) P=80m A=s 2 A=(20m) 2 A=400m 2 20 m
Triangle Perimeter P=a+b+c Area A= ½ bh b (base) h (height) ac
Ex: Find the perim. & area of the figure. P=a+b+c P=5ft+7ft+6ft P=18 ft A= ½ bh A= ½ (7ft)(4ft) A= ½ (28ft 2 ) A= 14ft 2 7 ft 5 ft 4 ft 6 ft
Circle Diameter d=2r Circumference C=2πr Area A=πr 2 diameter r a d i u s ** 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=πr 2 A=π(5in) 2 A=25π in 2 A≈78.5 in i n