Topic 1 - Congruency
Definitions:
Congruent figures - have the exact same size and shape
Corresponding parts - the specific sides and angles from each figure that are congruent to one another. ie: if Triangle ABC is congruent to Triangle DEF, then Angle A is congruent to Angle D and Side AB is congruent to Side DE.
Third Angles Theorem - If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent.
Reflexive Property - a figure, side, or angle is congruent to itself. ie Side AB is congruent to side AB.
Symmetric Property - If a = b then b = a
Transitive Property - If a = b and b = c, then a = c.
Congruent figures - have the exact same size and shape
Corresponding parts - the specific sides and angles from each figure that are congruent to one another. ie: if Triangle ABC is congruent to Triangle DEF, then Angle A is congruent to Angle D and Side AB is congruent to Side DE.
Third Angles Theorem - If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent.
Reflexive Property - a figure, side, or angle is congruent to itself. ie Side AB is congruent to side AB.
Symmetric Property - If a = b then b = a
Transitive Property - If a = b and b = c, then a = c.
Helpful Hints:
The order that you name a triangle matters. The congruent pieces must be in the same position.
The order that you name a triangle matters. The congruent pieces must be in the same position.
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Topic 2 - SSS
Definitions:
Side-Side-Side (SSS) Congruence - If three sides of one triangle are congruent to three sides of a second triangle, then the triangles are congruent.
Side-Side-Side (SSS) Congruence - If three sides of one triangle are congruent to three sides of a second triangle, then the triangles are congruent.
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Topic 3 - SAS and HL
Definitions:
Included Angle - the between two sides
Side-Angle-Side (SAS) Congruence - 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 triangles are congruent.
Hypotenuse-Leg (HL) Congruence - If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of a second triangle, then the triangles are congruent.
Included Angle - the between two sides
Side-Angle-Side (SAS) Congruence - 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 triangles are congruent.
Hypotenuse-Leg (HL) Congruence - If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of a second triangle, then the triangles are congruent.
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Topic 4 - ASA and AAS
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Topic 5 - CPCTC and Proofs
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Topic 6 - Overlapping Triangles
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