Download Chapter 9 9-1: Squares and Square Roots: Objectives: Find squares

Chapter 9
9-1: Squares and Square Roots:
Objectives:
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Find squares and square roots.
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Estimate Square roots.
VOCABULARY:
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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:
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Identify and compare numbers in the real number system.
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Solve equations by finding square roots.
VOCABULARY:
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Irrational Numbers: Numbers that are not repeating or terminating decimals
Real Numbers: The set of rational and irrational numbers together.
Notes:
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Classify numbers into different sets.
9-3: Angles:
Objectives:
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Classify angles as acute, right, obtuse or straight.
VOCABULARY:
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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:
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Find the missing angle measure of a triangle.
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Classify triangles by angles and by sides.
VOCABULARY:
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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:
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Use the Pythagorean Theorem to find the length of a side of a right triangle.
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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:
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Solving a right triangle is using the Pythagorean Theorem to find the length of a missing side of a right triangle.
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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:
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Use the Distance Formula to determine lengths in a coordinate plane.
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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:
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Identify corresponding parts and find missing measures of similar triangles.
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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:
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The corresponding angles have the same measure.
The corresponding sides are proportional.