Congruence of Triangles and Proof
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| all sides will marked congruent to the corresponding sides of a second triangle | ||
| all sides and all angles of the first triangle will be marked congruent to the corresponding sides and angles of the second triangle | ||
| two SIDES and an INCLUDED ANGLE will be marked congruent (the angle is formed by the two sides) | ||
| two ANGLES and an INCLUDED SIDE will be marked; the side is between the two angles | ||
| two angles and a non-included side will be marked congruent; the side is opposite one angle | ||
| then you have two congruent segments | ||
| then you have two congruent segments | ||
| then you have two congruent angles | ||
| then you have either alternate interior angles or corresponding angles (both pairs are congruent) or you have same-side interior angles (angles are supplementary) | ||
| Sum of the 2 small sides > largest side | ||
| Corresponding Parts of Congruent Triangles are Congruent | ||
| Polygons that have congruent corresponding parts: The corresponding angles are congruent AND the corresponding sides are congruent. | ||
| For right triangles, if the hypotenuse and a leg of one triangle are congruent to the corresponding parts of a second triangle, the triangles are congruent. Compare to SSA, which only works in right triangles. | ||
| Compare to SAS Postulate: the right angle is the included angle | ||
| Compare to AAS: the right angle is one of the angles | ||
| Compare to ASA for the leg between the right angle and acute angle OR compare to AAS for the leg opposite the acute angle. The right angle is one of the angles. |