Unit 5 Vocabulary

Third Angle Theorem

• If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent.

• If two angles of one triangle are equal to the third angle of another triangle, then the triangles are congruent.

• The sum of the angles in a triangle is always 180 degrees, regardless of the triangle's shape.

• If two angles of a triangle are acute, then the third angle must be obtuse.

Congruence Transformation

• A transformation that preserves the size and shape of a figure.

• A transformation that changes the size but not the shape of a figure.

• A transformation that alters the shape but not the size of a figure.

• A transformation that distorts the figure completely.

Side-Side-Side Congruence

• If three angles of one triangle are congruent to three angles of another triangle, then the triangles are congruent.

• If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.

• If the perimeter of one triangle is equal to the perimeter of another triangle, then the 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 triangles are congruent.

Angle-Side-Angle Congruence

• If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the 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 triangles are congruent.

• If two angles of one triangle are congruent to two angles of another triangle, then the triangles are congruent.

• If the sum of the angles in one triangle is equal to the sum of the angles in another triangle, then the triangles are congruent.

Angle-Angle-Side Congruence

• If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, then the 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 triangles are congruent.

• If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar but not necessarily congruent.

• If the corresponding sides of two triangles are proportional, then the triangles are congruent.

Hypotenuse-Leg Congruence

• In right triangles, if the hypotenuse and one leg of one triangle are congruent to the hypotenuse and one leg of another triangle, then the triangles are congruent.

• In right triangles, if two legs of one triangle are congruent to two legs of another triangle, then the triangles are congruent.

• In right triangles, if the hypotenuse is longer than one leg, then the triangles are congruent.

• In right triangles, if the angles are congruent, then the triangles are congruent.

Triangle Inequality Conjecture

• The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

• The sum of the lengths of all three sides of a triangle is equal to the length of the longest side.

• The sum of the lengths of any two sides of a triangle is less than the length of the third side.

• The lengths of all three sides of a triangle must be equal.

Side-Angle-Side Congruence

• If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the 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 triangles are congruent.

• If two sides of one triangle are congruent to two sides of another triangle, then the triangles are congruent.

• If the angles of one triangle are congruent to the angles of another triangle, then the triangles are congruent.

Hinge Theorem

• If two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first is larger than the included angle of the second, then the third side of the first is longer than the third side of the second.

• If two sides of one triangle are congruent to two sides of another triangle, then the two triangles are congruent.

• If two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first is smaller than the included angle of the second, then the third side of the first is shorter than the third side of the second.

• If two triangles have the same perimeter, then they are congruent.