Geometry Postulates and Theorems Ch. 4 and 5

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Side-Side-Side

If all three sides of one triangle are congruent to all three sides of a second triangle, then the two triangles are congruent

Side-Angle-Side

If two sides and the included angle of one triangle are congruent to two sides and the included side of a second triangle, then the two triangles are congruent

Angle-Side-Angle

If two sides and the included angle of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent

Triangle Sum Theorem

The sum of the measures of the interior angles of a triangle must add up to 180 degrees

Third Angles Theorem

If two angles of one triangle are congruent to two angles of a second triangle, then the third angles are also congruent

Exterior Angles Theorem

The measure of the exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles

Exterior Angle Inequality

The measure of the exterior angle of a triangle is greater than the measure of either of the two remote interior angles

Base Angles Theorem

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

Base Angles Theorem Converse

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

HL Congruence Theorem

If two lines are cut by a transversal such that the pairs of alternate interior angles are congruent, then the lines are parallel

Midsegment Theorem

The segment connecting the mid points of two sides of a triangle is parallel to the third side and half its length

Scalene Triangle

A triangle with no equal sides

Isosceles Triangle

A triangle with two equal sides

Equilateral Triangle

A triangle in which all three sides are congruent

Acute Triangle

A triangle where all three angles are less than ninety degrees

Equiangular Triangle

A triangle where all three angles are congruent

Right Triangle

A triangle where one of the angles is ninety degrees

Obtuse Triangle

A triangle where one of the sides is over ninety degrees

Parts of a right triangle

Legs and hypotoneus

CPCTC

States that corresponding parts of congruent triangles are congruent

Triangle Midsegment

A segment passing through the midpoint of 2 sides of a triangle

Included Angle

The angle where to sides meet

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