33 terms

# Triangle Congruence by ASA and AAS

Angle Side Angle Postulate Angle Angle Side Postulate More Key Terms for this Chapter
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Angle Side Angle Postulate
If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent
Angle Angle Side Postulate
If two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle, then the two triangles are congruent.
Triangle Congruence
SSS, SAS, ASA, AAS
Postulate
A statement that describes a fundamental relationship between the basic terms of geometry.
Triangles
A FIGURE WITH THREE SIDES AND THREE ANGLES
Proof
A logical argument in which each statement you make is supported by a statement that is accepted as true.
Writing A Proof
paragraph proof
Congruent Triangles
are triangles whose corresponding angles and sides are congruent. (They are exactly the same size and shape.)
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
Theorem
A statement that can be proven
Right Angle
A 90° Angle
Obtuse Angle
A 180° Angle
Acute Angle
An Angle Less Than 90°
Triangle
A shape that's total equals 180°
Can be Obtuse, Scalene, Right or Equilateral
Two Column Proof
a type of proof written as numbered statements and reasons that show the logical order of an argument
Flow Proof
a type of proof that uses arrows to show flow of a logical argument statements are connected by arrows to show how each statement comes before it. and each reason is written below the statement it justifies
Corresponding Angles
Angles (as well as other figures) that appear in the same position, have the same information but occur in different places
Congruent Corresponding Angles
if a line intersects two parallel lines, the corresponding angles are congruent (the same)
Method
A systematic plan based on a set of principles used in presenting material for instruction .
Logical Reasoning
the idea that there are principles governing correct or reliable inferences
Parallel Sides
Sides the same distance apart so they never intersect
Transversal
- A line that intersects 2 or more lines
- A line that intersects two or more coplanar lines at different points
Angle Angle Side Theorem
If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of a second triangle, then the two triangles are congruent.
Angle Side Angle Theorem
Given a correspondence between triangles such that two pairs of corresponding angles are congruent and their included sides are congruent, then the triangles are congruent
Included Angles
An angle is included by two sides if the two sides coincide with the sides of the angle.
Coincide
To be in the same place or occur at the same time.
Side Angle Side Postulate
Two triangles are congruent if 2 sets of corresponding sides and their included angles are congruent., Given a correspondence between triangles such that two pairs of corresponding sides are congruent and their included angles are congruent, then the triangles are congruent
(SAS)
Side Side Side Postulate
If three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.
Side Angle Side Theorem
If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent
Side Side Side Theorem
Given a correspondence between triangles such that 3 pairs of corresponding sides are congruent, then the triangles are congruent
Reflexive Property
A quantity is congruent (equal) to itself. a = a
If and Then Statement
A Hypothesis (Educated Guess) and then Proof of what you found.
Corresponding Parts
If two figures are congruent, then any pair of corresponding parts is congruent.