Discovering Geometry Chapter 4 Conjectures

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Triangle Sum Conjecture

The sum of the measures of the angles in every triangle is
180°. (Lesson 4.1)

Third Angle Conjecture

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. (Lesson 4.1)

Isosceles Triangle Conjecture

If a triangle is isosceles, then its base angles are congruent. (Lesson 4.2)

Converse of the Isosceles Triangle Conjecture

If a triangle has two congruent angles, then it is an isosceles triangle. (Lesson 4.2)

Triangle Inequality Conjecture

The sum of the lengths of any two sides of a triangle is greater than the length of the third side. (Lesson 4.3)

Side-Angle Inequality Conjecture

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. (Lesson 4.3)

Triangle Exterior Angle Conjecture

The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles. (Lesson 4.3)

SSS Congruence Conjecture

If the three sides of one triangle are congruent to the three sides of another triangle, then the triangles are congruent. (Lesson 4.4)

SAS Congruence Conjecture

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. (Lesson 4.4)

ASA Congruence 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. (Lesson 4.5)

SAA Congruence Conjecture

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. (Lesson 4.5)

Vertex Angle Bisector Conjecture

In an isosceles triangle, the bisector of the vertex angle is also the altitude and the median to the base. (Lesson 4.8)

Equilateral/Equiangular Triangle Conjecture

Every equilateral triangle is equiangular. Conversely, every equiangular triangle is equilateral. (Lesson 4.8)

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