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Transcript
Chapter 9 9-1: Squares and Square Roots: Objectives: Find squares and square roots. Estimate Square roots. VOCABULARY: Perfect Square: Squares of whole numbers. Square Root: One of two equal factors of a number Radical Sign: Used to indicate a square root: _________ 9-2: The Real Number System: Objectives: Identify and compare numbers in the real number system. Solve equations by finding square roots. VOCABULARY: Irrational Numbers: Numbers that are not repeating or terminating decimals Real Numbers: The set of rational and irrational numbers together. Notes: Classify numbers into different sets. 9-3: Angles: Objectives: Classify angles as acute, right, obtuse or straight. VOCABULARY: Ray: has one endpoint and extends in one direction. Line: Extends in both directions and does not end. Angle: Two rays that have a common endpoint. Vertex: The common endpoint in an angle. Side: The rays that make up an angle. Degree: Common unit for measuring angles. Acute Angle: an angle that is greater than 0 degrees but less than 90 degrees. Right Angle: an angle that measures 90 degrees Obtuse Angle: An angle that measures more than 90 degrees but less than 180 degrees. Straight Angle: An angle that measures 180 degrees. 9-4: Triangles Objectives: Find the missing angle measure of a triangle. Classify triangles by angles and by sides. VOCABULARY: Triangle: a figure formed by three line segments that intersect only at their endpoints. Acute Triangle: has all acute angles Obtuse Triangle: has one obtuse angle Right Triangle: has one right angle Scalene Triangle: no congruent sides Equiangular Triangle: all angle are equal and have a measure of 60 degrees. Isosceles Triangle: at least two sides congruent Equilateral Triangle: All sides are congruent Notes: The sum of the measures of the angles of a triangle is 180 degrees. 9-5: The Pythagorean Theorem Objectives: Use the Pythagorean Theorem to find the length of a side of a right triangle. Use the converse of the Pythagorean Theorem to determine whether a triangle is a right triangle. Notes: Picture of a right triangle: The Pythagorean Theorem: If a triangle is a right triangle, then the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. Picture and Symbols: Solving a right triangle is using the Pythagorean Theorem to find the length of a missing side of a right triangle. The hypotenuse is the LONGEST side of a right triangle and it is opposite the right angle. Converse of the Pythagorean Theorem: You can use this to determine if a triangle is a right triangle. It is simply the reverse of the Pythagorean Theorem: 9-6: The Distance and Midpoint Formula: Objectives: Use the Distance Formula to determine lengths in a coordinate plane. Use the Midpoint Formula to find the midpoint of a line segment on the coordinate plane. VOCABULARY: Distance Formula: Formula used to find the length of a segment in the coordinate plane. It is based on the Pythagorean Theorem. Midpoint: The point that is halfway between the endpoints of a line segment. Midpoint Formula: Formula used to find the coordinates of the midpoint of a line segment in the coordinate plane. NOTES: Formulas: 9-7: Similar Triangles and Indirect Measurement Objectives: Identify corresponding parts and find missing measures of similar triangles. Solve Problems involving indirect measurement using similar triangles. VOCABULARY: Similar Triangles: Triangles that have the same shape but not necessarily the same size. Symbol for Similar: ________ Notes: Similar Triangles have corresponding angles and corresponding sides. Corresponding Parts of Similar Triangles: If two triangles are similar: The corresponding angles have the same measure. The corresponding sides are proportional.