## Geometry ch.4

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lilstu1488  on March 13, 2012

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# Geometry ch.4

 congruent polygons2 polygons whose corresponding sides and angles are congruent
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#### Definitions

congruent polygons 2 polygons whose corresponding sides and angles are congruent
what two "Angle-Side Combos" don't work? AAA & ASS
Why doesn't AAA work? infinite solutions
Why doesn't ASS work? two solutions
Define an Included side a side whose endpoints are the vertexes of the angles we are dealing with
Define an Included angle an angle whose vertex is the shared endpoint of both sides.
Side-angle-side tri. con. post. 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.
Side-side-side if three sides of one triangle are congruent two three sides of another triangle, then they are congruent.
Angle-side-Angle If two angles and their included side of one triangle are congruent to 2 angles and their included sides of a second triangle, then they are congruent.
Angle-Angle-Side If two angles and their non-included sides of one triangle are congruent to the corresponding angles and non-included side of the other triangle, then they are congruent.
CPCTC corresponding parts of congruent triangles are congruent
what is used to prove two triangles congruent? angles and sides
Isosceles Triangle a triangle with at least 2 congruent sides.
Equilateral Triangle a triangle with all congruent sides
Isosceles Triangle theorem if a triangle has 2 congruent sides, the then angles opposite those congruent sides, are congruent as well.
Converse of the isosceles triangle theorem if two angles of a triangle are congruent, then the sides opposite those angles are congruent.
legs the two congruent sides of an isosceles triangle
base the non congruent side of an isosceles triangle
base angles the angles opposite the legs
vertex angle the angle formed by the two legs
Hypotenuse leg Theorem if a leg and the hypotenuse of a right triangle are congruent to the corr. leg and hypotenuse of a second right triangle, then the two triagles are congruent.
The bisector of the vertex angle of an isosceles triangle is... the perpendicular bisector of the base
corollary a statement that follows immediately from a theorem
If a triangle is equilateral.. it is equiangular too (and vice versa)

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