Chapter 4 Flashcards
1st true statement
since congruent triangles have same shape, their corresponding angles are congruent
2nd true statement
since congruent triangles have the same size, their corresponding sides are congruent
congruent triangles
2 triangles are congruent if and only if their vertices can be matched up so that the corresponding parts (angles and sides) of the triangles are congruent
common side
a side that shares both congruent figures
SSS Postulate
if 3 sides of 1 triangle are congruent to 3 sides of another triangle, then the triangles are congruent
SAS Postulate
if 2 sides and the included angle of 1 triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent
ASA Postulate
if 2 angles and the included side of 1 triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent
perpendicular line to a plane
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
legs
congruent sides of an isosceles triangle
base
third side of isosceles triangle
base angles
angles at the end of the base
vertex angle
angle opposite the base in an isosceles triangle
the isosceles triangle theorem
if 2 sides of a triangle are congruent, then the angles opposite those sides are congruent
or
base angles of an isosceles triangle are congruent
corollary 1
an equilateral triangle is also equiangular
corollary 2
an equilateral triangle has three 60 degree 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 2 angles of a triangle are congruent, then the sides opposite those angles are congruent
corollary 4
an equiangular triangle is also equilateral
AAS Theorem
if 2 angles and a non-included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent
hypotenuse
side opposite the right angle in a right triangle
legs
other two sides of a right triangle
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
median
segment in a triangle from a vertex to the midpoint of the opposite side
altitude
perpendicular segment in a triangle from a vertex to the line that contains the opposite side
perpendicular bisector
a line that is perpendicular to the segment at its midpoint
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
distance from a point to a line
length of the perpendicular segment from the point to the line
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
