Geometry Test #2

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Angle relationships and polygons

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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.