## (Geometry) Chapter 4

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Mole-Easter  on April 29, 2012

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# (Geometry) Chapter 4

 Proving Two Segments or Two Angles Are Equal1. 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.
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#### Definitions

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.

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