Honors Geometry Unit 4

Triangle sum conj.

The measure all 3 angles in a triangle add up to 180

Auxiliary line

The blue line

Isosceles triangle conj.

If a triangle is isosceles, then it has 2 congruent sides

Converse of iso triangle conj.

Triangle has 2 congruent sides, the its isosceles

Triangle inequality conj.

The sum of the lengths of any 2 sides of a triangle is greater than the length of the 3rd side.

Angle Inequality relationships

The largest angle of a triangle is opposite the longest side.

The smallest angle of a triangle is opposite the shortest side.

Triangle Exterior Angle Conj.

The measure of an exterior angle of a triangle is equal to the sum of its 2 remote interior angles.

SSS:Side-Side-Side

3 pairs of congruent sides

Does work

Can only fit one way

SAS - Side - Angle - Side

Works

2 pairs of congruent sides and 1 pair of congruent angles

Must be sandwiched to work

ASA: Angle - Side - Angle

2 Congruent angles and 1 congruent side

Sandwiched

Does work

SAA: Side - Angle - Angle

2 congruent angles and 1 congruent side

Not sandwiched

ASS: Angle - Side - Side

Doesn’t work

Right angle is an exception

HL(hypotenuse leg) congruency

AAA: Angle - Angle - Angle

3 congruent angles

Doesn’t work

Dilation

CPCTC

Corresponding Parts of Congruent Triangles are Congruent