Chapter 4 Review Booklet By: James Murphy Pg1- Classifying Triangles Pg2- Angle Sum Theorem, 3rd Angle Theorem, And Exterior Angle Sum Theorem Pg3- Solving Problems Involving Congruent Triangles Pg4- SSS And SAS Pg5- ASA And AAS Pg6- Proving Right Triangles Are Congruent Pg7- Coordinate Proofs
Classifying Triangles By Sides
Scalene-
Isosceles-
EqualateralBy Angles
Acute-
Obtuse-
Right-
Angle Sum Theorem, 3rd Angle Theorem, And Exterior Angle Sum Theorem Angle Sum Theorem- The sum of the measures of the angles of a triangle is 180째 Third Angle Theorem- If 2 angles of a triangle are congruent to 2 angles of another triangle, then the third pair of angles are congruent.
In this case, angles T and Q are congruent, and angles U and R are congruent, so that means angles S and P are congruent.
Exterior Angle Sum Theorem- The measure of an exterior angle is the sum of its remote interior angles.
Solving Problems Involving Congruent Triangles Congruent Triangles- If and only if corresponding parts are congruent.
Triangle ABC is congruent to Triangle DEF Angles Angle A is congruent to Angle D Angle B is congruent to Angle E Angle C is congruent to Angle F
Segments Segment AB is congruent to Segment DE Segment BC is congruent to Segment EF Segment AC is congruent to Segment DF
SSS and SAS Side-Side-Side Postulate- If 3 sides of a triangle are congruent to 3 sides of another triangle, those triangles are congruent by SSS.
Side-Angle-Side Postulate- If 2 sides of a triangle are congruent to 2 corresponding sides of another triangle and the included angles are congruent, then those triangles are congruent by SAS.
ASA and AAS Angle-Side-Angle Postulate- If 2 angles of a triangle and included side are congruent to 2 angles and included side of another triangle, the triangles are congruent by ASA.
Angle-Angle-Side Postulate- If 2 angles and their non included side of a triangle are congruent to 2 angles and the non included side of another triangle then those triangles are congruent by AAS.
Proving Right Triangles Are Congruent Hypotenuse-Leg Theorem
Leg-Angle Theorem
Leg-Leg Theorem
Hypotenuse-Leg Theorem
Coordinate Proofs
In this case, the coordinates would be; B- (0,0) C- (a,0) A-(b,c)