Chapter 4 Flashcards
Equilateral triangle
Has three congruent sides
Isosceles triangle
Has at least two congruent sides
Scalene triangle
Has no sides congruent
Congruent triangles
Two triangles are congruent if there is a correspondence between their angles and sides such that corresponding angles are congruent and corresponding sides are congruent .
Acute triangle
Has three acute angles
Equiangular triangle
If these angles are all congruent, then the triangle is also equiangular
Right triangle
Has exactly one right angle
Obtuse triangle
Has exactly one of obtuse angle
Vertex
Point of intersection of two sides
Adjacent side
Two sides that share a common vertex
Opposite side
Any side opposite a given angle
Right triangle- legs
The sides adjacent to the right angle
Right triangle
Hypotenuse
The side opposite the right angle
Isosceles triangle -legs
If it has only two congruent sides, then the two congruent sides are the legs
Isosceles triangle
Base
The third side of the triangle
Properties of congruent triangles
- Every triangle is congruent to itself
- If triangle ABC is congruent to triangle PQR, then triangle PQR is congruent to ABC
- If triangle ABC = triangle PQR and triangle PQR = TUV, then triangle ABC = triangle TUV
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)
•an angle that forms a linear pair with an interior angle
Triangle sum Theorem
The sum of the measures of the interior angles of a triangle is 180°
Third angles theorem
If two angles of one triangle are congruent to two angles of a second triangle, then the third angles are also congruent
The aCute angles of a right triangle…
Are complementary
Exterior angles theorem
The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote (nonadjacent) interior angles.
Exterior angles inequality theorem
Measure of an exterior angle of a triangle is greater than the measure of either the two remote (nonadjacent) inferior angles
Postulate 17: side – side – side congruence postulate
If three sides of one triangle are congruent to three sides of a second triangle, then the triangles are congruent
Postulate 18: side – angle – side congruence postulate
If two sides and the included angles of one triangle are congruent to two sides and the included angle of a second triangle, then the triangles are congruent
Partial at 19: angle – side – angle congruence postulate
If two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle, then the two angles are congruent.
There are 4.7: angle – angle – side congruence theorem•••
If two angles and a non-included side of one triangle are congruent to two angles and the corresponding not included side of the second triangle, then the two triangles are congruent
CPCTC
CP CTC is an abbreviation for corresponding parts of congruent triangles are congruent
Base angles
The two angles that have the base as a part of one side are the base angles
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 of 4.8: if a triangle is equilateral,
Then it is also equiangular
Corollary to theorem 4.9: if a triangle is equiangular,
Then it is also equilateral
Hypotenuse – leg congruence theorem
If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and leg of a second triangle, then the two triangles are congruent
