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27 Cards in this Set
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 Back
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 nonincluded 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."
