Chapter 4 Vocabulary - Discovering Geometry

Triangle Sum Conjecture

• 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
• The sum of the measures of the angles in every triangle is 180°
• A side of a triangle between two given angles
• The sum of the lengths of any two sides of a triangle is greater than the length of the third side

Tags

CCSS.8.G.A.5

Auxiliary line

• an extra line or segment added to a diagram that helps prove a conjecture
• The sum of the measures of the angles in every triangle is 180°
• If two angles and a non-included side of one triangle are congruent to the corresponding angles and side of another triangle, then the triangles are congruent
• A style of proof in which the statements are written in the left-hand column and the reasons are written in the right-hand column.

Legs of an Isosceles Triangle

• The two sides of an isosceles triangle that are equal in length
• The two interior angles that do not share a vertex with the exterior angle
• An angle formed between two given sides of a triangle
• Congruent Parts of Congruent Triangles are Congruent

Isosceles Triangle Conjecture

• The two angles adjacent (next) to the base and opposite the legs of an isosceles triangle
• If two angles and a non-included side of one triangle are congruent to the corresponding angles and side of another triangle, then the triangles are congruent
• The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles
• If a triangle is isosceles, then its base angles are congruent

Tags

CCSS.8.G.B.7

Adjacent interior angle

• If a triangle has two congruent angles, then it is an isosceles triangle
• The sum of the measures of the angles in every triangle is 180°
• 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
• The interior angle that forms a linear pair with a given exterior angle of a triangle

Tags

CCSS.8.G.A.5

Included angle

• An angle formed between two given sides of a triangle
• A side of a triangle between two given angles
• In a triangle, if one side is longer than another side, then the angle opposite the longer side is larger than the angle opposite the shorter side
• The two interior angles that do not share a vertex with the exterior angle

Included side

• Congruent Parts of Congruent Triangles are Congruent
• The sum of the lengths of any two sides of a triangle is greater than the length of the third side
• A style of proof in which the statements and reasons are presented in paragraph form.
• A side of a triangle between two given angles

Tags

CCSS.HSG.CO.B.7

Remote interior angles (of the exterior angle of a triangle)

• The two interior angles that do not share a vertex with the exterior angle
• The interior angle that forms a linear pair with a given exterior angle of a triangle
• If two angles of one triangle are equal in measure to two angles of another triangle, then the third angle in each triangle is equal in measure to the third angle in the other triangle
• The sum of the measures of the angles in every triangle is 180°

Tags

CCSS.8.G.A.5

Third Angle Conjecture

• the angle between the two congruent sides (legs) of an isosceles triangle
• If two angles of one triangle are equal in measure to two angles of another triangle, then the third angle in each triangle is equal in measure to the third angle in the other triangle
• A side of a triangle between two given angles
• The sum of the lengths of any two sides of a triangle is greater than the length of the third side

Tags

CCSS.8.G.A.5

Converse of the Isosceles Triangle Conjecture

• The sum of the lengths of any two sides of a triangle is greater than the length of the third side
• the non-congruent side of an isosceles triangle, opposite the vertex angle
• If a triangle has two congruent angles, then it is an isosceles triangle
• 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

Tags

CCSS.HSG.CO.C.9