Warm-up: Using the Pythagorean Theorem

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Presentation transcript:

Warm-up: Using the Pythagorean Theorem Find the value of x. Give your answer in simplest radical form. a2 + b2 = c2 Pythagorean Theorem 22 + 62 = x2 Substitute 2 for a, 6 for b, and x for c. 40 = x2 Simplify. Find the positive square root. Simplify the radical.

A Quick History Lesson

I can… … name and identify the basic tools of Geometry. Geometry Vocabulary I can… … name and identify the basic tools of Geometry. The easiest thing to do is to plug in 1 and -1 (or 2 and -2) if you get the same y, then it’s Even. If you get the opposite y, then it’s Odd. If you get different y’s, then it’s Neither.

Point An undefined Geometric term that represents a location. A dot is used to symbolize it and it is thought of as having no length, width, or thickness. Point A Point B

Line An infinite set of points with no thickness and its length continues in two opposite directions indefinitely. Written as

Collinear/Non-collinear Points Three or more points that lie on the same line. Points A, F, and B are collinear. Three or more points that do not lie on the same line. Points B, G, and H are non- collinear Points A, F, and G are non- collinear.

Line Segment A part of a line between two points on the line. Written as

Ray A part of a line that begins at a point and continues forever in one direction. Written as

Plane A flat, two-dimensional surface that extends infinitely far.

Angle A figure created by two distinct rays that share a common endpoint (Vertex). The angle is <𝐴𝐵𝐶 <𝐵 <𝐶𝐵𝐴 < α

Circle The set of points on a plane equidistant from a point in a plane.

Parallel Line Two lines are parallel if they lie in the same plane and do not intersect. Written as 𝐴𝐵 // 𝐶𝐷

Perpendicular Line Two lines are perpendicular if they intersect to form right angles. 𝐴𝐵 ⊥ 𝐶𝐷

Transformation The mapping, or movement, of all points of a figure in a plane according to a common operation, such as a translation, rotation, or reflection. -----------------

Pre-image A figure before a transformation has taken place. -----------------

Image The result of a transformation. ------------

Translation A transformation that slides each point of a figure the same distance in the same direction. ---------------------

Reflection A transformation of a figure that creates a mirror image, “flips,” over a line. Reflection over the X-axis.

Reflection Line (line of reflection) A line that acts as a mirror so that corresponding points are the same distance from the mirror.

Rotation A transformation that turns a figure about a fixed point through a given angle and a given direction, such as 90o clockwise.

Angle of Rotation The amount of rotation (in degrees) of a figure about a fixed point such as the origin. --------

Dilation Transformation that changes the size of a figure, but not the shape. The size change is determined by the scale factor.

Scale Factor The ratio of any two corresponding lengths of the sides of two similar figures. -----------------