(Geometry) Chapter 4
|Proving Two Segments or Two Angles Are Equal|| 1. Find two triangles in which the two sides or the two angles are corresponding parts.|
2. Prove that the two triangles are congruent.
3. State that the two parts are equal.
|Perpendicular Bisector||A bisector of a segment that is perpendicular to the segment|
|Theorem 1||Any point on the perpendicular bisector of a segment is equidistant from the endpoints of the segment.|
|Theorem 2||Any point that is equidistant from the endpoints of a segment is onn the perpendicular bisector of the segment.|
|Altitude||A segmentm drawn from any vertex, perpendicular to the line that contains the opposite side.|
|Altitude (Acute Triangle)||The lines meet inside the triangle.|
|Altitude (Right Triangle)||The lines meet at the vertex of the right angle.|
|Altitude (Obtuse Triangle)||The lines meet outside the triangle.|
|Circumscribed About||When each vertex of a triangle is a point on a circle.|
|Perpendicular Bisector (Acute Triangle)||Bisectors meet inside the triangle.|
|Perpendicular Bisector (Right Triangle)||Bisectors meet on triangle.|
|Perpendicular Bisector (Obtuse Triangle)||Bisectors meet outside the triangle.|
|Circumscribed circle||Triangle or other polygon is inside the circle.|
|Inscribed circle||Circle is inside the triangle or other polygon.|
|Theorem 3||If two side of a triangle are equal, then the angles opposite those sides are equa|
|Corollary||An equilateral triangle is also equiangular, and each angle has a measure of 60 degrees.|
|Ways To Prove Two Angles Are Equal|| 1. Show that they are corresponding parts of congruent triangles.|
2. Show that they are opposite two equal sides of a triangle.
3. Show that they are corresponding angles or alternate interior angles of parallel lines.
|Theorem 4||If two angles of a triangle are equal, then the sides opposite those angles are equal|
|Prove Two Segments Are Equal|| 1. Show that they are corresponding parts of congruent triangles.|
2. Show that they are opposite two equal angles of a triangle.
|The Triangle Inequality||In a triangle, the sum of the lengths of any two sdes must be greater than the length of the third side.|