Triangle Properties - Ch 4 Triangle Sum Conjecture The sum of the measures of the angles of a triangle is…. …180 degrees. C-17 p. 199.

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Presentation transcript:

Triangle Properties - Ch 4 Triangle Sum Conjecture The sum of the measures of the angles of a triangle is…. …180 degrees. C-17 p. 199

Triangle Properties - Ch 4 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. C-18 p. 200

Triangle Properties - Ch 4 Isosceles Triangle Conjecture If a triangle is isosceles, then…. …its base angles are congruent. C-19 p. 205

Triangle Properties - Ch 4 Converse of the Isosceles Triangle Conjecture If a triangle has two congruent angles, then…. …it is an isosceles triangle. C-20 p. 206

Triangle Properties - Ch 4 Triangle Inequality Conjecture The sum of the lengths of any two sides of a triangle is …. ….greater than…. C-21 p. 214 …the length of the third side.

Triangle Properties - Ch 4 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. C-22 p. 215

Triangle Properties - Ch 4 Triangle Exterior Angle Conjecture The measure of an exterior angle of a triangle …. ….is equal to the sum of the measures of the remote (non-adjacent) interior angles. C-23 p. 216

Triangle Properties - Ch 4 SSS Congruence Conjecture If the three sides of one triangle are congruent to the three sides of another triangle, then…. C-24 p. 220 …the triangles are congruent.

Triangle Properties - Ch 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…. C-25 p. 221 …the triangles are congruent.

Triangle Properties - Ch 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…. C-26 p. 225 …the triangles are congruent.

Triangle Properties - Ch 4 AAS 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…. C-27 p. 226 …the triangles are congruent.

Triangle Properties - Ch 4 Vertex Angle Bisector Conjecture In an isosceles triangle, the bisector of the vertex angle is also…. C-28 p. 242 …the altitude... …and… …the median to the base.

Triangle Properties - Ch 4 Equilateral/Equiangular Triangle Conjecture Every equilateral triangle is… C-29 p. 243 …equiangular... …and, conversely, every equiangular triangle is… …equilateral.