Unit 3

Leg

A leg of a triangle is one of its sides.

Reflexive property

A quantity is congruent (equal) to itself. a = a

Scalene triangle

A scalene triangle is a triangle that has three unequal sides, such as those illustrated above.

Right triangle

A triangle that has a 90 degree angle.

Acute triangle

An acute triangle is a triangle with all three angles acute (less than 90°).

Equiangular triangle

An equiangular triangle is a triangle where all three interior angles are equal in measure.

Obtuse triangle

An obtuse triangle is one with one obtuse angle (greater than 90°) and two acute angles.

Triangle inequality theorem

Any side of a triangle must be shorter than the other two sides added together.

CPCTC

Corresponding Parts of Congruent Triangles are Congruent

Transitive property

If a=b and b=c, then a=c

Triangle largest side theorem

If one side of a triangle is longer than another side, then the angle opposite the longer side will be larger than the angle opposite the shorter side.

Triangle congruency

If two pairs of sides of two triangles are equal in length, and the included angles are equal in measurement, then the triangles are congruent.

Isosceles Triangle theorem

If two sides of a triangle are congruent, then the angles opposite those sides are congruent.

AAS

Triangles are congruent if two pairs of corresponding angles and a pair of opposite sides are equal in both triangles.

SSS

Triangles are congruent if all three sides in one triangle are congruent to the corresponding sides

SAS

Triangles are congruent if any pair of corresponding sides and their included angles are equal in both triangles.

ASA

Triangles are congruent if any two angles and their included side are equal in both triangles.

Justification

the fact that is said to prove that something is true

Midpoint formula

(x₁+x₂)/2, (y₁+y₂)/2

Exterior angle theorem

The exterior angle theorem is Proposition 1.16 in Euclid's Elements, which states that the measure of an exterior angle of a triangle is greater than either of the measures of the remote interior angles.

Triangle largest angle theorem

The longest side is always opposite the largest interior angle.

Hypotenuse

The longest side of a right triangle. The side opposite the right angle.

Substitution property

The substitution property of equality makes algebra possible.

Triangle sum theorem

The sum of the measures of the interior angles of a triangle is 180 degrees

HL

Two right triangles are congruent if the hypotenuse and one corresponding leg are equal in both triangles.

Two column proof

a type of proof written as numbered statements and reasons that show the logical order of an argument

Equilateral triangle

an equilateral triangle is a triangle in which all three sides are equal.

Isosceles triangle

an isosceles triangle is a triangle that has two sides of equal length.

Pythagorean theorem

a²+b²=c²

Symmetric property

if a=b, then b=a