Geometry Honors - PROOFS: Reflexive Property, Vertical Angles, Midpoint/Bisector/Medians, Angle Bisectors/CPCTC, Altitudes, Isosceles Triangles, Parallel Lines, Similarity

What is needed for a HL congruency proof?

1. right angle 2. hypotenuse 3. one of the legs must be congruent

Which methods do NOT prove congruency?

AAA and SSA

Angle Bisector (Reasons)

Angle bisector divides an angle into two congruent angles.

Base angles of an isosceles triangle are ____________________.

Base angles of an isosceles triangle are COGRUENT

CSSTP

Corresponding sides of similar triangles are proportional

PPMEPE

In a proportion, the product of the means equals the product of the extremes

Legs of an isosceles triangle are ____________________.

Legs of an isosceles triangle are CONGRUENT

Midpoint, Line Bisector, and Median (Reasons)

Midpoint, Line Bisector, and Median divide a segment into two congruent segments.

Vertical angles (Reasons)

Vertical angles are congruent.

Reflexive Property

When two angles share the same side or triangle.

AAA (DOESNT PROVE CONGRUENCY)

angle angle angle

AAS

angle angle side

ASA

angle side angle

Vertical angles will usually exist in a diagram that looks like a ____________________.

bowtie

Altitudes and Perpendicular Lines form ________________________________.

congruent right angles

Congruent angles have ________________________.

congruent supplements

Parallel lines cut by _________________________________________________________________________________.

cut by a transversal form alternate interior angles

HL

hypotenuse leg

The second column of a proof states the ______________________.

reasons

Right triangles contain __________________________. * * * HL ONLY EXISTS WITH RIGHT TRIANGLES * * *

right angles

SAS

side angle side

SSA (DOESNT PROVE CONGRUENCY)

side side angle

SSS

side side side

The first column of a proof states the ______________________.

statements

PROVING LINES ARE PARALLEL: If alternate interior angles are congruent, ____________________________________________________________________.

then segments cut by the transversal are parallel.

Angle bisector divides an angle into ________________________________.

two congruent angles

Midpoint, Line Bisector, and Median all divide a segment into ___________________________________.

two congruent segements