Geometry Test #2

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Information about Geometry Test #2
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Published on November 5, 2008

Author: mslaverty

Source: authorstream.com

Geometry : Geometry What you need to know for Test #2 Vertical Angles : Vertical Angles Two angles whose sides form two pairs of opposite rays. Identifying Angles : Identifying Angles A transversal is a line that intersect two coplanar lines at two distinct points. Slide 4: Eight angles have been formed by the transversal t and the lines m and h. t m h 1 2 4 5 3 6 7 8 On the diagram below, line t is the transversal intersecting the lines h and m at two distinct points. Alternate Interior Angles : Alternate Interior Angles Nonadjacent interior angles that lie on opposite sides of the transversal. Alternate Interior Angles : Alternate Interior Angles Angle 8 and angle 4 are alternate interior angles. Angle 3 and angle 7 are also alternate interior angles. t m h 1 2 4 5 3 6 7 8 Same-Side Interior Angles : Same-Side Interior Angles Angles which lie on the same side of the transversal between the two lines intersected by that transversal. Same-Side Interior Angles : Same-Side Interior Angles Angle 3 and angle 4 are same-side interior angles. Angle 7 and angle 8 are also same-side interior angles. t m h 1 2 4 5 3 6 7 8 Corresponding Angles : Corresponding Angles Angles that lie on the same side of the transversal in a corresponding position as related to the lines intersected by the transversal. Corresponding Angles : Corresponding Angles Angle 1 and angle 7 are corresponding angles. Angle 2 and angle 4 are also corresponding angles. Angle 3 and angle 5 are also corresponding angles. Angle 8 and angle 6 are also corresponding angles. t m h 1 2 4 5 3 6 7 8 Properties of Parallel Lines : Properties of Parallel Lines Corresponding Angles Postulate If a transversal intersects two parallel lines, then corresponding angles are congruent. Properties of Parallel Lines : Properties of Parallel Lines Alternate Interior Angles Theorem If a transversal intersects two parallel lines, then alternate interior angles are congruent. Properties of Parallel Lines : Properties of Parallel Lines Same-Side Interior Angles Theorem If a transversal intersects two parallel lines, then same-side interior angles are supplementary. 180° 180° Converse Theorems : Converse Theorems Converse of the Corresponding Angles Postulate If two lines and a transversal form corresponding angles that are congruent, then the two lines are parallel. Converse Theorems : Converse Theorems Converse of the Alternate Interior Angles Theorem If two lines and a transversal form alternate interior angles that are congruent, then the two lines are parallel. Converse Theorems : Converse Theorems Converse of the Same-Side Interior Angles Theorem If two lines and a transversal form same-side interior angles are supplementary, then the two lines are parallel. 180° 180° Relating Parallel Lines : Relating Parallel Lines If two lines are parallel to the same line, then they are parallel to each other. Triangle Angle-Sum Theorem : Triangle Angle-Sum Theorem The sum of the measures of the angles of a triangle is 180. Classifying Triangles by the Angles : Classifying Triangles by the Angles Equiangular Acute Right Obtuse All angles are congruent. All angles are acute. One angle is right. One angle is obtuse. Classifying Triangles by the Segments : Classifying Triangles by the Segments Equilateral Isosceles Scalene All sides are congruent. At least two sides are congruent. No sides are congruent. Triangle Exterior Angle Theorem : Triangle Exterior Angle Theorem The measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles. Polygons : Polygons A polygon is a closed plane figure with at least three sides that are segments. Polygons : Polygons A polygon is convex if it has no diagonal with points outside of the polygon. A polygon is concave if it has at least one diagonal with points outside the polygon. Polygon Angle-Sum Theorem : Polygon Angle-Sum Theorem The sum of the measures of the angles of an n-gon is (n-2)180. Polygon Exterior Angle-Sum Theorem : Polygon Exterior Angle-Sum Theorem The sum of the measures of the exterior angles of a polygon, one at each vertex, is 360.

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