Geometry Acceptable Shortened Forms

Theorems

Conditional Form Shortened Form

If two angles are right angles, then they are congruent. right ∠s ⇒ ≅ If two angles are straight angles, then they are congruent. st. ∠s ⇒ ≅ If two angles form a linear pair, then they are supplementary. linear pair ⇒ supp

If angles are supplementary to the same angle, then they supps of same ∠ ⇒ ≅ are congruent. If angles are supplementary to congruent angles, then they supps of ≅ ∠s ⇒ ≅ are congruent. If angles are complementary to the same angle, then they comps of same ∠ ⇒ ≅ are congruent. If angles are complementary to congruent angles, then they comps of ≅ ∠s ⇒ ≅ are congruent. If the same segment/angle is added to congruent Addition Prop. of ≅ segments/angles, then the sums are congruent. If congruent segments/angles are added to congruent Addition Prop. of ≅ segments/angles, then the sums are congruent. **Similarly, you may use Subtraction Prop of ≅ Subtraction Prop. of ≅ If segments/angles are congruent, then their like multiples Like multiples ≅ are congruent. If segments/angles are congruent, then their like divisions Like divisions ≅ are congruent. If two angles are vertical angles, then they are congruent. Vertical ∠s ⇒ ≅ (No “def. of vertical angles” step required) If angles/segments are congruent to the same or congruent Transitive Prop of ≅ angles/segments, then they are congruent. If angles/segments are congruent, then one may replace Substitution Prop. of ≅ the other. If two angles are supplementary and congruent, then supp + ≅ ⇒ rt ∠s they are right angles.

Definitions Shortened Form

A right angle is an angle whose measure is 90° rt. ∠ ⇒ 90° Congruent segments/angles have equal measures. ≅ ⇒ = meas. A midpoint divides a segment into two congruent mdpt. ⇒ 2 ≅ segs segments. A segment/angle bisector divides a segment/angle into bis ⇒ 2 ≅ segs/∠s two congruent segments/angles. Complementary angles are two angles whose sum is comp ⇒ rt ∠ a right angle (90°). Supplementary angles are two angles whose sum is supp ⇒ st ∠ a straight angle (180°). Perpendicular lines, rays, segments meet to form ⊥ ⇒ rt ∠s An altitude of a triangle is a line segment drawn from alt ⇒ ⊥ or alt ⇒ rt ∠ any vertex of the triangle to the opposite side, extended if necessary, and perpendicular to that side. (An altitude or alt ⇒ 90° ∠ of a triangle forms right [90°] angles with one of the sides.) A median of a triangle is a line segment drawn from med ⇒ mdpt or med ⇒ 2 ≅ segs any vertex of the triangle to the midpoint of the opposite side. (A median of a triangle divides into two congruent segments, or med ⇒ bisect or bisects the side to which it is drawn.) A scalene triangle is a triangle in which no two sides are scalene Δ ⇒ no sides ≅ congruent. An isosceles triangle is a triangle in which at least two sides isos Δ ⇒ legs ≅ are congruent. An equilateral triangle is a triangle in which all sides are equilateral Δ ⇒ all sides ≅ congruent. An acute triangle is a triangle in which all angles are acute Δ ⇒ all ∠s acute acute. An obtuse triangle is a triangle in which one angle is obtuse Δ ⇒ obtuse ∠ obtuse. A right triangle is a triangle in which one angle is right. right Δ ⇒ rt ∠ congruent.