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2020 Triangles
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Key Concepts:
Terms in this set (30)
SSS
Three sides of one triangle are congruent to three sides of another triangle.
SAS
Two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle.
ASA
Two angles and the included side of one triangle are congruent to two triangles and the included side of another triangle.
AAS
Two angles and the non-included side of one triangle are congruent to two angles and the non-included side of another triangle.
HL
The hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle.
Perpendicular Bisector
A line that forms 90 degree angles and cuts a segment in half. Any point on the perpendicular bisector is equidistant to the endpoints of the segment.
Angle Bisector
A ray or line that cuts an angle in half. Any point on the angle bisector is equidistant to the sides of the angle.
Corresponding parts of congruent triangles are congruent (CPCTC)
A theorem stating that if two triangles are congruent, then so are all corresponding parts.
Congruent Sides
Have the exact same length.
Vertex of an Angle
A corner point of an angle. For an angle, the vertex is where the two rays making up the angle meet.
Corresponding Sides
Two sides that are situated the same way in different objects.
Corresponding Angles
Two angles that are situated the same way in different objects.
Third Angles Theorem
If the 2 angles of one triangle are congruent to 2 angles of another triangle, then the third angles are congruent
Isosceles Triangle Theorem
If 2 sides of a triangle are congruent, then the angles opposite those sides are congruent
Converse of the Isosceles Triangle Theorem
If 2 angles of a triangle are congruent, then the sides opposite of the angles are congruent
Congruent
when two parts of a geometric figure have the same shape and size
Corresponding
geometric parts that are in the same position in different figures
Included side
A side that is between two angles in a triangle
In the figure, LM is the included side between angle L and angle M.
Included angle
An angle that is between two sides in a triangle
In the figure, angle N is the included angle between LN and MN.
Angle-Angle-Angle (AAA)
does NOT prove triangles congruent because the sides could be different lengths.
Side-Side-Angle (SSA)
does NOT prove triangles congruent
Congruent Triangles
3 pairs of corresponding angles are congruent and 3 pairs of corresponding sides are congruent.
Equiangular Triangle
A triangle whose angles are all congruent.
Scalene Triangle
A triangle that has no congruent sides.
Isosceles Triangle
A triangle with two congruent sides.
Equilateral Triangle
A triangle that has all three sides congruent.
Triangle Sum Theorem
The sum of the measures in a triangle is 180 degrees.
Exterior Angle Theorem
The sum of the remote interior angles is equal to the measure of the exterior angle.
Hinge Theorem
Longest side is opposite largest angle; same with smallest and middle
Triangle Inequality Theorem
The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
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