Chapter 9 Notes

9-1 Intro. To Geometry W T K H n  Name four Points.  Name four different segments.  Write five other names for line n.  Name five different rays.

9-1 Intro. To Geometry- Answers W T K H n  Name four Points. H,K, T, and W  Name four different segments. HT, WT, KT, WK  Write five other names for line n. WK, TK, KT, KW, TW  Name five different rays. TH, TW, TK, WK, KW

Intersecting, Parallel, and Skew Lines L K Q P M R S N Name all indicated segments -- That intersect MN. That are skew to MN.

Intersecting, Parallel, and Skew Lines-answers L K Q P M R S N Name all indicated segments -- That intersect MN. ML, NK, MR, NS That are skew to MN. PS, RQ, PK, QL

9-2 Angle Relationships and Parallel Lines Name vertical angles. Name adjacent angles. If m<8 = 20°, find measures of <5, <6, and <7.

9-2 Angle Relationships and Parallel Lines-answers Name vertical angles. 7,5; 8,6 Name adjacent angles. 5,8; 8,7;7,6; 6,5 If m<8 = 20°, find measures of <5, <6, and <7. m<5 = 160°, m<6 = 20°, m<7 = 160°

9-2 Angle Relationships and Parallel Lines p q Name adjacent angles. 2.Name vertical angles. 3.Name supplementary angles. 4.Name complementary angles. 5.Name congruent corresponding angles. 6.Name congruent alternate interior angles. p || q

9-2 Angle Relationships and Parallel Lines p q Name adjacent angles. 1,5; 1, 2; 2, 6; 6, 5 2.Name vertical angles. 3,8; 4,7; 2,5; 1,6 3.Name supplementary angles. 3,7; 4,8; 2,6; 5,6 4.Name complementary angles. none 5.Name congruent corresponding angles. 1,3; 5,7; 2,4; 6,8 6.Name congruent alternate interior angles. 2,7; 6,3 p || q

9-2 Angle Relationships and Parallel Lines (5x -18)° (4x+7)° 1.Write an equation. 2.Find x. 3.Find m<MNQ. 4.Find m<MNR. M R N Q P

9-2 Angle Relationships and Parallel Lines-answers (5x -18)° (4x+7)° 1.Write an equation. 5x - 18 = 4x Find x. x=25 3.Find m<MNQ. 107° 4.Find m<MNR. 73° M R N Q P

9-3 Classifying Polygons

9-3 Classifying Polygons- answers Isoceles acute Right isoscelesNot a polygon Equilateral acute parallelogram trapezoid Scalene obtuse

Classifying Quadrilaterals and polygons

Classifying Quadrilaterals and polygons-answers Regular Octagon parallelogram rhombus trapezoid Regular hexagon square Regular pentagon rectangle

9-5 Congruence Congruent figures: have the same size and shape and their corresponding parts have equal measure. A C B F E D <A is congruent to <F <B is congruent to <D <C is congruent to <E AC is congruent to FE AB is congruent to FD BC is congruent to DE ABC is congruent toFDE

Identifying Congruent Triangles SSS: Side-Side-Side SAS: Side-Angle-Side ASA: Angle-Side-Angle Examples: following slide.

Answers 9. <B congruent to <D BC congruent to DC <ABC congruent to <ECD ASA 10. JK congruent to JM LK congruent to LM JL congruent to JL SSS

9-6 Circles Circle: is a set of all points in a plane that are the same distance from a given point called the center of the circle. Radius: is a segment that has one endpoint at the center and the other point on the circle Diameter: is a chord that passes through the center of a circle. Chord: is a segment whose endpoints are on the circle.

Circumference of a Circle Circumference: the distance around a circle C = πd C = 2πr Find circumference of each circle. 1. Radius = 3.5 cm 2. Diameter = 1/2 yd 100 in. 3. Radius = 4 2/3 ft.

Circumference of a Circle - answers Circumference: the distance around a circle C = πd C = 2πr Find circumference of each circle. 1. Radius = 3.5 cm = 21.98cm 2. Diameter = 1/2 yd = 1 4/7 yd. 100 in. 3. Radius = 4 2/3 ft. = 29 1/3 ft. C=314in

Central Angles Central angle: is an angle whose vertex is the center of a circle. There are 360 o in a circle. Examples: Find central angle % = _____ degrees 2. 50% = _____ degrees 3. 1% = ______ degrees 4. 30% = ______ degrees 5. 18% = ______ degrees

Central Angles-answers Central angle: is an angle whose vertex is the center of a circle. There are 360 o in a circle. Examples: Find central angle % = __126___ degrees 2. 50% = _180____ degrees 3. 1% = ____4__ degrees 4. 30% = ___108___ degrees 5. 18% = ___65___ degrees

9-8 Translations Transformation: is a change of position or size of a figure Translation: is a transformation that moves points the same distance and in the same direction A’: means A prime B’: means B prime These are the new figures after they have been translated.

(1,4) (1,2) (-2,3)

Dilations Dilation: a transformation that changes the size of the figure but not usually the shape Scale Factor: how many times larger or smaller you will make the original figure

9-9 Symmetry and Reflections Reflectional Symmetry: when one half is a mirror image of the other half. Line of symmetry: divides a figure into 2 congruent halves. Reflection: is a transformation that flips a figure over a line of reflection

9-10 Rotations Rotations: is a transformation that turns a figure about a fixed point Center of rotation: this is the fixed point where a figure is turned Angles of rotation: the angle measure of the rotation Rotational symmetry: rotating a figure 180 o, or less, so that its image matches the original figure