Unit 2 Review! Objective: to review the concept of congruence Common Core State Standards: 8.G.1; 8.G.2; 8.G.5; 8.G.6; 8.G.7.

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Presentation transcript:

Unit 2 Review! Objective: to review the concept of congruence Common Core State Standards: 8.G.1; 8.G.2; 8.G.5; 8.G.6; 8.G.7

Types of Angles Matching! Transversal A line that cuts across two or more (usually parallel) lines Exterior angles that are on opposite sides of the transversal (equal to each other) Interior angles that are on opposite sides of the transversal (equal to each other) Alt Ext. Angles Alt Int. Angles Corr. Angles Angles in the same position with respect to the lines and transversal (equal to each other) Vertical Angles Angles that are opposite from each other formed by the intersection of 2 lines (equal to each other)

All About Triangles! x° y° z° The sum of the measures of the interior angles of a triangle is 180 ° x° + y° + z° = 180° The measure of an exterior angle of a triangle is equal to the sum of the measures of its two remote interior angles. x° y° p° x° + y° = p° Pythagorean Theorem: In a right triangle, the square of the lengths of the hypotenuse c is equal to the sum of the squares of the lengths of the legs a and b. a 2 + b 2 = c 2 a b c

Midpoint & Distance on the Coordinate Plane Midpoint Distance

Transformations The four main Transformations are: Translation (Slide)Reflection (Flip) Rotation (Turn)Dilation (Scale)

A translation is a transformation that slides a figure in any direction. Translation Rule: Ta,b (x, y) = (x + a, y + b) Example T0,4 (2, 3) = (2 + 0, 3 + 4) = (2, 7)

Rotation Rules: A rotation is a transformation that turns a figure about a fixed point called the center of rotation. The measure of the rotation is the angle of rotation.

Reflection Rules: Y axis: (x, y)  (-x, y) X-Axis: (x, y)  (x, -y) Y=X: (x, y)  (y, x) Y=-X: (x, y)  (-y, -x) A reflection is a transformation that flips a figure over a line of reflection. The distance from a point to the line of reflection is the same as the distance from the point's image to the line of reflection.

A dilation is a transformation that makes a figure larger or smaller. This means the two figures are similar (same shape/different size). A scale factor is the ratio of the side lengths of the image to the corresponding side lengths of the original figure. Dilation Rule: (x,y)  (kx, ky) k>1: enlargement 0<k<1: reduction

Let’s Practice! MAP PLUS BOOKLET QUESTIONS # 8, 18, 34, 36, 43, 44, 56, 64 Exit Ticket After reviewing and practicing Unit 2, rate yourself on how you feel about the same questions in the MAP Plus Book.