Shortcuts to Congruence
A "shortcut" conjecture involving two sides of a triangle & the angle between them being congruent to the corresponding parts of another triangle; used to prove the two triangles congruent.
What is Side-Angle-Side (SAS)?
It's what two lines are called if they cross to form right angles
What is Perpendicular?
It's what a triangle is called if no sides are congruent
What is Scalene?
It's the conjecture we use to show two angles are congruent in an Isosceles triangle
What is the Base Angles Theorem?
This is the only shortcut that doesn't need an angle
What is Side-Side-Side (SSS)?
It's what you can conclude if G is the midpoint of segment AB
What is "segment AG is congruent to segment GB"?
It's a triangle with an angle measuring between 90 and 180 degrees.
What is an Obtuse triangle?
It's a conjecture that can be used to determine if a triangle is possible with given side lengths
What is the Triangle Inequality Theorem?
It's the property used to show that if a=b and b=c, then a=c
What is the "Transitive Property of Equality" (Can you feel the logic flow?!)
These type of triangles have at least two congruent sides
What is Isosceles?
It's the minimum number of angle measures needed to know in an Isosceles triangle to find the other(s)
What is one?
It's how we know two right angles are congruent to each other
What is 'by definition!' (Also, the "Right Angle Congruence Theorem")
It's the property used to replace one value with another equivalent value
What is the Substitution Property?
Congruent angles directly across from each other where two lines intersect
What are vertical angles?
It's the "Statement" in a proof whose "Reason" or justification was ASA (or AAS or SAS or SSS or HL)
What is a Triangle Congruence Statement?
If we know two angle measures within a triangle, what can we logically conclude?
What is the 3rd angle? (--> third angles theorem)
It's the property used to show an object is congruent to itself
What is "shared side," a.k.a. the Reflexive Property of Congruence (like a mirror)?
In a triangle, it's what the sum of the two nonadjacent interior angles are equal to
What is the Exterior Angle?
It's what CPCTC stands for
What is Corresponding Parts of Congruent Triangles are Congruent?