11-1: Angle Relationships 4 ways to name angles –Use the vertex as the middle letter, and the point from each side (<ABC or <CBA) –Use the vertex only (<B) –Use a number (<1) Classify angles according to their measure. – Acute angle: less than 90° –Right angle: exactly 90° –Obtuse angle: between 90° and 180° –Straight angle: exactly 180°

11-1: Angle Relationships Angle relationships –A pair of angles is complementary if the sum of their measures is 90° The “c” for complementary is the curve of the “9” –A pair of angles is supplementary if the sum of their measures is 180° The “s” for supplementary is the curve of the “8”

11-2: Display Data in a Circle Graph Circle graph – a pie chart that displays information as a % If the data is not given to you in a percent: –Add all the values given to you ( = 250) –Divide the part by the whole & convert the decimal answer to a percent 50/250 = 0.2 = 20% 75/250 = 0.3 = 30% 125/250 = 0.5 = 50%

11-2: Display Data in a Circle Graph Degree measurement –Either convert your percent to a decimal or find the part divided by the whole as a decimal and multiply by % = 0.2 * 360 = 72° Percent of a number (% of a #) – Multiply the percent as a decimal by the number. –25% of 200 .25 x 200 = 50 If there were 12 million cars in the U.S. and 30% of the cars were in Texas, then 3.6 million cars were in Texas 30% = 0.3 * 12 = 3.6

11-3: Triangles Triangle – figure with 3 sides and 3 angles. The sum of the measures of a triangle is 180. Classify triangles using the angles or their sides. Congruent segments mean the sides have the same length. –Classify using Angles: Acute triangle: all acute angles Right triangle: 1 right angle Obtuse triangle: 1 obtuse angle –Classify using Sides: Scalene triangle: no congruent sides Isosceles triangle: 2 congruent sides Equilateral triangle: 3 congruent sides

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11-5: Quadrilaterals Quadrilateral – figure with 4 sides and 4 angles. The sum of the measures of the angles is 360. Classify quad. using their angles or sides. –Trapezoid: quad. with exactly one pair of parallel sides –Parallelogram: quad. With both pairs of opposite sides parallel and congruent –Rhombus: parallelogram with 4 congruent sides –Square: parallelogram with 4 right angles and 4 congruent sides –Rectangle : parallelogram with 4 right angles Use the most specific name that describes the quad.

11-5 continued

11-6: Similar Figures Similar Figures – figures that have the same shape but not necessarily the same size Corresponding sides/angles – sides or angles of similar figures that “match” Indirect measurement – uses similar figures to find the length, width or height of objects that are too difficult to measure directly

11-6: Similar Figures

11-7: Polygons & Tessellations Polygon – simple, closed figure formed by 3 or more straight lines. The lines will not cross. Regular polygon – a polygon that has all sides and angles congruent

Polygons are classified by the number of sides Tesselation – a repetitive pattern of polygons that fit together with no overlaps or holes. –The sum of the measures of the angles where the vertices meet is 360

Total angle measurements of polygons: –(# of Sides – 2) * 180 Individual angle measurement: –Total angle measurement divided by # of sides For example, a pentagon has 5 sides. –Total angle measurement = (5 – 2) * 180 = 540 –Each individual angle = 540 / 5 = 108

11-8: Translations Transformation – maps one figure onto another –The figure before the transformation is called the pre-image. After the transformation the figure is called the image. Translation – moving the figure without turning it, sliding a figure over Congruent figures – figures that have the same size and same shape, and the corresponding sides and angles have the same measure

11-8: Translations Prime Symbols - vertices in the transformed image A  A ′ B  B ′ C  C′ A ′ is read A prime

11-9: Reflections Symmetry – figures that match exactly when folded in half –Each fold is called a line of symmetry Reflection – transformation of a figure over a line called a line of reflection –An image and reflection are mirror images of each other with respect to the x-axis or y-axis

11-9: Reflections Reflection over the x-axis Reflection over the y-axis