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27 Cards in this Set

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Theorem: If 2 angles of a triangle are congruent...
then the sides opposite those angles are congruent
Corollary: An equiangular triangle is...
also equilateral
SAA Theorem
If two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent
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.
Hypotenuse
The side opposite the right angle of a right triangle.
Legs
The sides adjacent to the right angle of a right triangle.
Summary of possible ways to prove triangles are congruent:
All triangles- SSS, SAS, SAA, ASA
Right triangles- HL
Corollary: The bisector of the vertex angle of
an isosceles triangle is perpendicular to the base at its midpoint
SAS Postulate
If two sides & the included angles of one triangle are congruent to two sides & the included angle of another triangle, then the triangles are congruent.
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.
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
How do you prove two segments or two angles are congruent?
1. Identify two triangles in which the segments or angles are corresponding parts.
2. Prove that the triangles are congruent.
3. State that the two parts are congruent, using the reason
Corresponding parts of congruent triangles are congruent.
The Isosceles Triangle Theorem
If two sides of a triangle are congruent, then the angles opposite those sides are congruent.
Corollary: An equilateral triangle is
also equiangular
Corollary: An equilateral triangle has
three 60° angles
congruent
two figures that have the same size and shape
Two triangles are congruent if...
and only if their vertices can be matched up so that corresponding parts (sides and angles) of the triangles are congruent.
Polygons are congruent if and only if...
their vertices can be matched up so that corresponding parts are congruent
SSS Postulate
If 3 sides of one triangle are congruent to 3 sides of another triangle, then the triangles are congruent.
Complete the theorem: "If a point is equidistant from the endpoints of a segment...
then the point lies on the perpendicular bisector of the segment
Complete the theorem: "If a point lies on the bisector of an angle...
then the point is equidistant from the sides of the angle
Complete theorem: "If a point is equidistant from the sides of an angle...
then the point lies on the bisector of an angle."
Every triangle has 3 ______ and 3 _______
medians, altitudes
median of a triangle
a segment from a vertex to the midpoint of the opposite side
altitude of a triangle
is the perpendicular segment from a vertex to the line that contains the opposite side, in an acute triangle each of the 3 altitudes is inside the triangle, in a right triangle 2 of the altitudes are the legs and the third intersects the hypotenuse, in an obtuse triangle 2 altitudes are outside the triangle and the third altitude is inside
perpendicular bisector of a segment
is a line(ray or plane)that is pependicular to the segment at its midpoint
Complete the theorem:"If a point lies on the perpendicular...
bisector of a segment, then the point is equidistant from the endpoints of the segment."