Chapter 6 and 7 (IM2)

AAS theorem

Angle Angle Side theorem of congruence of triangles. Two congruent angles and one side that forms one of these angles also need to be congruent.

ASA theorem

Angle Side Angle Theorem of congruence of triangles. Two congruent angles and the side in between these two angles need to be congruent.

HL Theorem

Hypotenuse Leg Theorem of congruence of triangles. The hypotenuse and one of the legs of two right triangles need to be congruent so both triangles are congruent.

Converse of Isosceles Triangle Theorem

If two angles in a triangle are congruent, then the triangle is isosceles.

Reflexive Property

Mirror: AB = BA

SAS theorem

Side Angle Side theorem of congruence of triangles. Two congruent sides and the angle formed by these two sides need to be congruent.

SSS theorem

Side Side Side Theorem of congruence of triangles. Three congruent sides in both triangles.

Isosceles Triangle Theorem

The base angles in an isosceles triangle are congruent.

The Centroid of a Triangle

The medians of a triangle are concurrent at a point called the centroid that is two thirds of the distance from each vertex to the midpoint of the opposite side.

Mid Segment of a Trapezoid

The segment joining the midpoint of the legs of a trapezoid is parallel to the bases, and is length is one half the sum of the lengths of the base.

The Mid Segment Theorem

The segment joining the midpoint of two sides of a triangle is parallel to the third side, and its length is one half the length of the third side.

If a line passes through the midpoint of one side of a triangle and is parallel to another side

Then it cuts the third side of the triangle at its midpoint .

Transitive Property

Twins that are Triplets. AB = CD; CD = EF. Therefore, AB = EF

Symmetric Property

When it had an axis of symmetry that cuts an object in two congruent parts.

Vertical Angles

are angles opposite by the vertex and they are congruent.

Supplementary angles

are angles that add to 180 degrees.

Complementary angles

are angles that add to 90 degrees.

Supplements of congruent angles Complements of congruent angles

are congruent

Angles in a linear pair

are supplementary

If two parallel lines are cut by a transversal, then pairs of interior angles on the same side of the transversal

are supplementary. (Same Side Interior Angles Theorem)

Linear pair

are two angles that form a line.

The median through the vertex of an isosceles triangle

is also an altitude and an angle bisector.

The sum of the measures of the interior angles of a triangle

is equal 180. (Angle Sum Theorem)

The measures of an exterior angle of a triangle

is equal to the sum of the its remote interior angles. (Exterior Angle Theorem)

The perpendicular bisector of a segment

is the locus of the points equidistant from the endpoints of that segment.

CPCTC

means corresponding parts of congruent triangles are congruent.

Angle addition postulate

m∠1+m∠2=m∠AOB

If two lines are cut by a transversal and form interior angles on the same side

that are supplementary, then the two lines are parallel. (Converse of the Same Side Interior Angles Theorem)

If two parallel lines are cut by a transversal

then alternate interior angles are congruent. (Alternate Interior Angles Theorem)

If a transversal intersects two parallel lines

then corresponding angles are congruent (Corresponding Angles Postulate).

If a transversal and two lines form a pair of alternate interior angles that are congruent

then the lines are parallel. (Converse of Alternate Interior Angles Theorem)

If a transversal cuts two lines and forms a pair of corresponding angles that are congruent

then the two lines must be parallel (Converse of Corresponding Angles Postulate)

If two lines are parallel to the same line

then they are parallel to each other.

Through a given point not on a line

there exists exactly one line parallel to this line. (Parallel lines postulate)