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Transcript
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.