Chapter 4 Flashcards
equilateral
3 congruent sides.
Isosceles
At least two congruent sides.
Scalene
No congruent sides
Acute
3 acute angles
Equilangular
Acute triangle with 3 congruent angles.
Right
Exactly one right angle.
Obtuse
Exactly one obtuse angle.
Vertex
Point of Intersection of two sides.
Opposite Side
Any side opposite an angle.
Adjacent Sides
Any two sides that share a common vertex.
Legs (Of a Right Triangle)
Sides adjacent to the right angle.
Hypotenuse
Side opposite the right angle.
Legs (Of a Isosceles Triangle)
Two congruent sides
Base
Non-congruent side.
Properties of Congruent Triangles
- ) Reflexive POC applies to triangles
- ) Symmetric POC applies to triangles.
- ) Transitive POC applies to triangles.
Interior Angle
Angles formed by the sides of a figure, located in the interior of the figure.
Exterior Angle
An angle that is adjacent to an interior angle (Must form a linear pair).
Auxiliary Line
Line added to a geometric figure.
Triangle Sum Theorem
The sum of the measures of the interior angles of a triangle is 180 degrees.
Third Angles Theorem
If two angles of one triangle are congruent to two angles of a second triangle, then the third is congruent (There is no such thing as the third sides theorem).
Theorem 4.4
The acute angles of a right triangle are complementary.
Exterior Angle Theorem
The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles.
Exterior Angle Inequality Theorem
The measure of an exterior angle of a triangle is greater that the measure of either of the two non adjacent interior angles.
Side-Side-Side (SSS) Congruence Postulate
If three sides of one triangles are congruent to 3 sides of a second triangle, then the triangles are congruent.
Side-Angle-Side (SAS) Congruence Postulate
If two sides and the included angle of one triangle are congruent to 2 sides and the included angle of a second triangle, the the triangles are congruent.
Angle-Side-Angle Congruence Postulate
If two congruent angles and the included side of one triangle are congruent to two angles and the included side of a second triangle, then the triangles are congruent.
Angle-Angle-Side Congruence Theorem
If two angles and a non-included side of one triangle are congruent to two angles and the corresponding bin-included side of a second triangle, then the triangles are congruent (Can use the third angles theorem)
Base Angles
Two angles that have the base as part of one side.
Base Angles Theorem
If two sides of a triangle are congruent, then the angles opposite them are congruent.
Base Angles Converse Theorem
If two angles of a triangle are congruent, then the sides opposite them are congruent.
Corollary to Base Angles Theorem and Base Angles Converse
A triangle is equilateral if an only if it is equiangular.
Hypotenuse-Leg (HL) Congruence Theorem
If the hypotenuse and lef of one right triangle are congruent to the hypotenuse and leg of a second right triangle, the the two triangles are congruent.
Corresponding Parts of Congruent Triangles are Congruent (CPCTC)
Once two triangles are proven congruent, by definition, all remaining corresponding sides are angles are congruent.
