Geometry Ch 4 - Congruent Triangles Flashcards
Congruent Polygons
Have congruent corresponding parts – their matching sides and angles. Matching vertices are corresponding vertices. When you name them, always list corresponding vertices in the same order.
If two angles of one triangle are congruent to two angles of another triangle…
… then the third angles are congruent.
Side-Side-Side (SSS) Postulate
If the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent.
Side-Angle-Side (SAS) Postulate
If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.
Angle-Side-Angle (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 two triangles are congruent.
Angle-Angle-Side (AAS) Theorem
If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, then the triangles are congruent.
Isosceles Triangle Theorem
If two sides of a triangle are congruent, then the angles opposite those sides are congruent.
Converse of Isosceles Triangle Theorem
If two angles of a triangle are congruent, then the sides opposite the angles 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…
then the triangle is equiangular.
If a triangle is equiangular…
…then the triangle is equilateral.
Hypotenuse
In a right triangle, it is the side opposite the right angle, and is the longest side.
Legs
In a right triangle, it’s the sides that are NOT the hypotenuse.
Hypotenuse-Leg (HL) Theorem
If the hypotenuse and a leg of one right triangle are congruent tot he the hypotenuse and a leg of another right triangle, then the triangles are congruent.
