Name ______________________________________________ I) Theorems You Should Know Vertical Angles Theorem Congruent Supplements Theorem Congruent Complements Theorem Alternate Interior Angles Theorem, AIA Same-Side Interior Angles Theorem, CIA Alternate Exterior Angles Theorem, AEA) Converse of Alternate Interior Angles Theorem Converse of Same-Side Interior Angles Theorem Converse of Alternate Exterior Angles Theorem In a plane, if a two lines are parallel to the same line, then they are parallel to each other. In a plane, if a two lines are perpendicular to the same line, then they are parallel. In a plane if a line is perpendicular to one of two parallel lines, then it is also perpendicular to the other. Triangle Angle Sum Theorem Triangle Exterior Angle Theorem Polygon Angle Sum Theorem Polygon Exterior Angle-Sum Theorem If two angles of one triangles are congruent to two angles of another triangle then the third angles are congruent Angle-Angle-Side (AAS) Theorem Isosceles Triangle Theorem Converse of Isosceles Triangle Theorem The bisector of a vertex angle of an isosceles triangle is the perpendicular bisector of the base. Hypotenuse Leg (HL) Theorem II) Postulates You Should Know Segment Addition Postulate Angle Addition Postulate Corresponding Angles Converse of Corresponding Angles Postulate Side-Side-Side (SSS) Postulate Side-Angle-Side (SAS) Postulate Angle-Side-Angle (ASA) Postulate

III) Terms You Should Know Collinear Points Hypotenuse Congruent Segments Legs of a Right Triangle Coplanar Line Line Segment Midpoint Opposite Ray Parallel Lines Parallel Planes Plane Point Ray Segment Skew Lines Alternate Exterior Angles Alternate Interior Angles Same Side Interior Angles Corresponding Angles Same Side Exterior Angles Transversal Segment Bisector Angle Angle Bisector Straight Angle Acute Angle Obtuse Angle Right Angle Vertex Adjacent Angles Vertical Angles Complementary Angles Supplementary Angle Exterior Angle of a Polygon Remote Interior Angles of a Triangle Polygon Concave Polygon Convex Polygon Regular Polygon Corresponding Parts of Congruent Triangles are Congruent Legs of an Isosceles Triangle Vertex Angle of an Isosceles Triangle Base Angles of an Isosceles Triangle Base of an Isosceles Triangle IV) Properties You should know Properties of Equality Addition Subtraction Multiplication Division Reflexive Symmetric Transitive Substitution Distributive Properties of Congruence Classify Triangles Acute Obtuse Right Scalene Isosceles Equilateral Equiangular Classify Polygons Triangle Quadrilateral Pentagon Hexagon Heptagon Octagon Nonagon

Name ___________________________________________ GEOMETRY Review Sheet Test 4-5 to 4-7 Name ___________________________________________ I) Solve for x. 1) 2) (23x + 8)° 8x + 3 (3x – 1)° 3x 6x – 3 3) 4) 25° 4x° 34° x° II) Vocabulary

III) Which triangles are congruent. How do you know III) Which triangles are congruent. How do you know? (AAS, ASA, SSS, SAS or HL) 5) P Q T S R 6) Hint: there are two sets of congruent triangles here.

IV) Write a proof 7) B A C D 8) B X   C A K 9) L P Q

Name ___________________________________________ GEOMETRY Review Sheet Test 4-5 to 4-7 Answers Name ___________________________________________ 1) x = 6 2) x = 1 3) x = 14 4) x = 90 5) QPR  SRP HL 6) DEA  BAE SAS AND CEB  CAD

7) Given BDA &  BDC are right angles Def of Perpendicular   BAC is isosceles Given Def of Isosceles Triangle    BDA   BDC HL CPCTC   Reflexive Prop of Congruence   OR Given BDA &  BDC are right angles Def of Perpendicular  BDA   BDC All right angles Are congruent   BAC is isosceles Given Base Angles of Isosceles Triangle Are Congruent  A   C  BDA   BDC AAS CPCTC   Reflexive Prop of Congruence   8) Given    XBA   BAC AIA  BAC   BCA Transitive Prop of Congruence Converse of Isosceles  Theorem Definition of Isosceles Triangle   ABC is isosceles  XBA   BCA Given

9)  PKL   QKL  PKL   QKL < P  < Q Given Given   Given    PKL   QKL  PKL   QKL < P  < Q Given Def of Bisector SAS CPCTC   Reflexive Prop of Congruence