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SMCHS
Geometry B
Mr. Ricks
Chapter 4:
Vocabulary
Congruent figures: two or more figures with the same size and shape
Corresponding angles:
Corresponding sides:
Congruent Triangles: two triangles are congruent if and only if their vertices can be
matched up so that the corresponding parts (angles and sides) of the triangle are
congruent.
Congruent Polygons: two polygons are congruent if and only if their vertices can be
matched up so that their corresponding parts are congruent.
A line and a plane are perpendicular if and only if they intersect and the line is
perpendicular to all lines in the plane that pass through the point of intersection.
In an isosceles triangle, the congruent sides are called legs and the third side is called the
base.
In a right triangle the side opposite the right angle is called the hypotenuse. The other
two sides are called legs.
Median of a triangle: a segment from a vertex to the midpoint of the opposite side.
Altitude of a triangle: the perpendicular segment from a vertex to the line that contains
the opposite side.
Perpendicular Bisector of a segment: a line that is perpendicular to the segment at its
midpoint.
Postulates
Postulate 12: SSS Postulate
If three sides of one triangle are congruent to three sides of another triangle, then
the triangles are congruent.
Postulate 13: SAS Postulate
If two sides and the included side of one triangle are congruent to two sides and
the included angle of another triangle, then the triangles are congruent.
Postulate 14: ASA Postulate
If two angles and the included side of one triangle are congruent to two angles
and the included side of another triangle, then the triangles are congruent.
Theorems
Theorem 4.1: The Isosceles Triangle Theorem
If two sides of a triangle are congruent, then the angles opposite those sides are
congruent.
Corollary 1:
An equilateral triangle is also equiangular.
Corollary 2:
An equilateral triangle has three 60 angles.
Corollary 3:
The bisector of the vertex angle of an isosceles triangle is perpendicular to
the base at its midpoint.
Theorem 4.2:
If two angles of a triangle are congruent, then the sides opposite those angles are
congruent.
Corollary:
An equiangular triangle is also equilateral.
Theorem 4.3: AAS Theorem
If two angles and a non-included side of one triangle are congruent to the
corresponding parts of another triangle, then the triangles are congruent.
Theorem 4.4: HL Theorem
If the hypotenuse and a leg of one right triangle are congruent to the
corresponding parts of another right triangle, then the triangles are congruent.
Theorem 4-5:
If a point lies on the perpendicular bisector of a segment, then the point is
equidistant from the endpoints of the segment.
Theorem 4-6:
If a point is equidistant from the endpoints of a segment, then the point lies on the
perpendicular bisector of the segment.
Theorem 4-7:
If a point lies on the bisector of an angle, then the point is equidistant from the
sides of the angle.
Theorem 4.8:
If a point is equidistant from the sides of an angle, then the point lies on the
bisector of the angle.