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Concepts 10-11 Notes
Congruent Triangles
Concept 10 – Classifying Triangles and Triangle Angle-­‐Sum (Section 4.1) ANGLE Classifications SIDE Classifications Acute: Scalene: Obtuse: Isosceles: Right: Equilateral: Equiangular: Theorem 4.1 – Triangle Sum Theorem The sum of the measures of the angles of a triangle is ________. Theorem 4.2 – Exterior Angle Theorem The measure of each exterior angle of a triangle equals the sum of the measures of the two _________________________________________. m∠1 = m∠A + m∠B Corollary to the Triangle Sum Theorem The acute angles of a right triangle are ___________________________. m∠A + m∠C = 90 Concept 11 – Apply Congruence and Triangles (Section 4.2) Congruent Polygons: -­‐ Have corresponding ___________ that are congruent -­‐ Have corresponding ____________ that are congruent Congruence Statement: -­‐ a statement saying that two figures are congruent -­‐ corresponding parts must be lined up Theorem 4.3 -­‐ Third Angle Theorem If two angles of one triangle are congruent to two angles of another triangle, then the third angles _______________________________________. Concept 11 – Congruent Triangles (Sections 4.3-­‐4.5) Side-­‐Side-­‐Side Postulate (SSS) If the sides of one triangle are congruent to the sides of another triangle, then __________________________________. Side-­‐Angle-­‐Side Postulate (SAS) If ________________________________________ of a triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent. Angle-­‐Side-­‐Angle Postulate (ASA) If ________________________________________of a triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent. Angle-­‐Angle-­‐Side Postulate (AAS) If two angles and a ___________________ side of a triangle are congruent to two angles and the non included side of another triangles, then the triangles are congruent. Hypotenuse-­‐Leg Theorem (HL) If the _______________________________ of one right triangle is congruent to the hypotenuse and leg of another right triangle, then the triangles are congruent. BAD PROOFS – these do not work Concept 11 – Using Congruent Triangles (Section 4.6) CPCTC: _________________________________________________________________ Example: Using CPCTC Concept 11 – Isosceles and Equilateral Triangles (Section 4.7) Parts of an Isosceles Triangle Legs: Base: Base Angles: Vertex Angle: Theorem 4.7 – Base Angles Theorem If two sides of a triangle are congruent, then the two angles opposite those sides are ____________________. Theorem 4.8 -­‐ Converse of the Base Angles Theorem If two angles of a triangle are congruent, then the two sides opposite those angles are ___________________. Corollary to the Base Angles Theorem If a triangle is equilateral , then it is _____________________. Corollary to the Converse of the Base Angles Theorem If a triangle is equiangular, then it is _____________________.