Download Side-Angle-Side Congruence (SAS)

AM1 Congruent Triangle / Quadrilateral Proof List
Substitution Property
Properties of Equality
Addition,
Subtraction,
Multiplication,
Division
Def. Perpendicular Lines
Sum of Angles in a Triangle = 180
Reflexive Property
Def. of a Midpoint
Linear Pair
Vertical Angles
Corresponding Angles
Alternate Interior Angles
Alternate Exterior Angles
Same Side Interior
Same Side Exterior
Side-Angle-Side Similarity (SAS~)
Side-Side-Side Similarity (SSS~)
Angle-Side-Angle Similarity (AA)
Side-Angle-Side Congruence (SAS)
Side-Side-Side Congruence (SSS)
Angle-Side-Angle Congruence (ASA)
Hypotenuse-Leg Congruence (HL)
CPCTC
Corresponding Parts of
Congruent Triangles are
Congruent
Def. of a Parallelogram
Def. of a Rectangle
Def. of a Square
Def. of a Rhombus
Def. of a Kite
Def. of an Isosceles Triangle
AM1 Congruent Triangle / Quadrilateral Proof List
Def. Perpendicular Lines
Form a right angle (90)
Sum of Angles in a Triangle = 180
Substitution Property
Example: If 1 = 2 and 2 = 3
Then 1 = 3 by substitution
Properties of Equality (Addition, Subtraction,
Multiplication and Division)
Example: If 1 + 2 = 2 + 3
Then 1 = 3 by Subtraction Prop. Of Eq.
Reflexive Property
A line is equal to itself. An angle is equal to itself.
Def. of a Midpoint
A midpoint is a point that cuts a segment into two
segments of equal length.
Linear Pair
2 Angles formed from a line. They add to 180
Vertical Angles
Angles formed when lines cross. Opposite angles
congruent
AM1 Congruent Triangle / Quadrilateral Proof List
Lines (j & k) cut by transversal (t):
This diagram is used for corresponding, alternate interior,
alternate exterior, same side interior, and same side
exterior angles.
Corresponding Angles
If the lines j & k are parallel…
Then angles in same relative position are congruent.
Corresponding Angles
If corresponding angles are congruent,
Then the lines j & k are parallel.
Alternate Interior Angles
If the lines j & k are parallel…
Then alternate interior angles are congruent.
Alternate Interior Angles
If the alternate interior angles are congruent,
Then the lines j & are parallel.
Same Side Interior
Same Side Interior angles are supplementary.
AM1 Congruent Triangle / Quadrilateral Proof List
Side-Angle-Side Congruence (SAS)
If an angle in one triangle is congruent to an angle of
another triangle and the sides that make this angle are
congruent, the triangles are congruent.
Side-Angle-Side Similarity (SAS~) if the two sides differ by
a common scale factor.
Side-Side-Side Congruence (SSS)
If all sides in one triangle equal all sides in another
triangle, the triangles are congruent.
Side-Side-Side Similarity (SSS~) if all sides differ by a
common scale factor.
Angle-Side-Angle Congruence (ASA)
If two angles in one triangle are congruent to two angles in
a second triangle and one corresponding side is congruent
in each triangle, the triangles are congruent.
Angle-Angle Similarity (AA) if the two angles in one
triangle match two angle in another triangle.
Hypotenuse-Leg Congruence (HL)
If the hypotenuse and one leg of one right triangle are
congruent to the hypotenuse and one leg of a second right
triangle, the triangles are congruent.
CPCTC
Corresponding Parts of Congruent Triangles are
Congruent
If you know (or have proven) that two triangles are
congruent, then their corresponding parts are congruent.
AM1 Congruent Triangle / Quadrilateral Proof List
Def. of a Parallelogram
Quadrilateral with…
1. Opposite Sides Parallel, or
2. Opposite Sides Congruent, or
3. Opposite Angles Congruent, or
4. Diagonals Bisect, or
5. One pair of sides both Parallel and Congruent.
Def. of a Rectangle
4 Right Angles
A rectanlge is a parallelogram.
Def. of a Square
Def. of a Rhombus
4 Right Angles and 4 Congruent Sides
A square is a rectangle, rhombus and parallelogram.
4 Congruent Sides
A rhombus is a parallelogram.
Def. of a Kite
2 pairs of adjacent congruent sides
Def. of an Isosceles Triangle
At least one pair of congruent sides.
or
At least one pair of congruent angles.