Chapter 4 Overview Flashcards
congruent figures
have the same size and shape; you can slide, flip, or turn
one so that it fits exactly on the other one
congruent polygons
have congruent corresponding parts – their matching
sides and angles
*When you name congruent polygons, you must list corresponding vertices in
the same order.
Theorem 4-1 – Third Angles Theorem
If 2 angles of one ∆ are ≅ to 2 ∠’s of another ∆, then the third ∠’s are ≅.
Postulate 4-1 – Side-Side-Side (SSS) Postulate
If the three sides of one ∆ are ≅ to the three sides of another ∆, then the 2
∆’s are ≅.
Postulate 4-2 – Side-Angle-Side (SAS) Postulate
If 2 sides and the include angle of one ∆ are ≅ to 2 sides and the included ∠
of another ∆, then the 2 ∆’s are ≅.
included angle
he angle between two sides of a triangle
included side
The common leg of two angles
Postulate 4-3 – Angle-Side-Angle (ASA) Postulate
If 2 ∠’s and the included side of one ∆ are ≅ to 2 ∠’s and the included side of
another ∆, then the 2 ∆’s are ≅.
Theorem 4-2 – Angle-Angle-Side (AAS) Theorem
If 2 ∠’s and a nonincluded side of one ∆ are ≅ to 2 ∠’s and
the corresponding nonincluded side of another
triangle, then the ∆’s are ≅.
CPCTC
If you know 2 triangles are congruent, then you know that every pair of their
corresponding parts is also congruent.
Isosceles triangle
triangle that has 2 sides of equal length
vertex angle
angle formed by the 2 ≅ legs
base angles
other 2 angles
legs
congruent sides of an isosceles triangle
base
the side not ≅ to another side
Theorem 4-3 – Isosceles Triangle Theorem
If 2 sides of a ∆ are ≅, then the ∠’s opposite those sides are ≅.
Theorem 4-4 – Converse of the Isosceles Triangle Theorem
If 2 ∠’s of a ∆ are ≅, then the sides opposite those ∠’s are ≅.
Theorem 4-5
If a line bisects the vertex ∠ of an isosceles ∆, then the line is also the
perpendicular bisector of the base.
corollary
theorem that can be proved easily using another theorem
Corollary to Theorem 4-3
If a ∆ is equilateral, then the ∆ is equiangular.
Corollary to Theorem 4-4
If a ∆ is equiangular, then the ∆ is equilateral.
System of Equations
2 or more equations
Substitution
1) Solve for x or y in one equation. Choose a variable with coefficient of 1.
2) Substitute it into the other equation.
3) Solve.
Elimination
1) Eliminate x or y by adding the equations together.
2) Solve.
hypotenuse
side opposite the right angle
- longest side of the ∆
leg
the other 2 sides of right ∆
Theorem 4-6 – Hypotenuse-Leg (HL) Theorem
If the hypotenuse and a leg of one right triangle are congruent to the
hypotenuse and a leg of another right triangle, then the triangles are congruent.
