Previous Unit Constructions. Next Unit Polygons. Brian McCall. Thank you for watching the video. Start Your Free Trial Learn more. Brian McCall Univ. Geometry Triangles. The ASA rule states that: If two angles and the included side of one triangle are equal to two angles and included side of another triangle, then the triangles are congruent.
The AAS rule states that: If two angles and a non-included side of one triangle are equal to two angles and a non-included side of another triangle, then the triangles are congruent. If three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent. If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.
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.
If two angles and the non-included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent. HL stands for " H ypotenuse, L eg" t he longest side of a right-angled triangle is called the "hypotenuse" , the other two sides are called "legs".
See Pythagoras' Theorem to find out more. If the hypotenuse and one leg of one right-angled triangle are equal to the corresponding hypotenuse and leg of another right-angled triangle, the two triangles are congruent. Therefore, if two corresponding pairs of angles in two triangles are congruent, then the remaining pair of angles is also congruent.
So the triangles are congruent. As an example, if 2 triangles are congruent by SSS, then we also know that the angles of 2 triangles are congruent. Two triangles are congruent if their corresponding sides are equal in length and their corresponding interior angles are equal in measure. Corresponding sides and angles mean that the side on one triangle and the side on the other triangle, in the same position, match.
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