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Download Theorems you should know!! Below is a list of MOST of the
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Transcript
Theorems you should know!! Below is a list of MOST of the Theorems we have learned thus far. You need to understand and know how to apply these theorems. For each Theorem listed below, fill in the blank with the appropriate terminology.. You must also draw a diagram next to each one to illustrate what the theorem listed is actually saying. 1. Segment Addition Postulate If B is between A and C, then ________________________. 2. Angle Addition Postulate If S is in the interior of PQR, then, ____________________________________________. 3. Pythagorean Theorem In a right triangle, the _________ of the ______________ of the lengths of the legs is equal to the _______________ of the length of the ______________________. 4. Linear Pair Theorem If two angles are supplementary, then they are ________________________________. 5. Vertical Angles Theorem Vertical angles are _____________________. 6. Corresponding Angles Postulate If two _________________ lines are cut by a _______________________, then the pairs of corresponding angles are __________________________. 7. Alternate Interior Angles Theorem If two __________________ lines are cut by a _______________________, then the pairs of alternate interior angles are __________________________. 8. Alternate Exterior Angles Theorem If two _________________ lines are cut by a ________________________, then the pairs of alternate exterior angles are _________________________. 9. Same-Side Interior Angles Theorem If two _______________ lines are cut by a ___________________________, then the pairs of sameside interior angles are ______________________________. 10. Parallel Lines Theorem In a coordinate plane, two lines are parallel if and only if _______________________________. 11. Perpendicular Lines Theorem In a coordinate plane, two lines are perpendicular if and only if ___________________________ ____________________________________________________________. Vertical and horizontal lines are always _____________________________. 12. Triangle Sum Theorem The __________ of the ______________ measures of a triangle is ______________. The acute angles of a right triangle are ___________________________________. The measure of each angle of an equiangular triangle is ___________. 13. Exterior Angle Theorem The measure of an __________________ angle of a triangle is equal to the __________ of the measures of its _____________________________________________. 14. Third Angles Theorem If two angles of one triangle are congruent to two angles of another triangle, then ____________ _________________________________________________________________________. 15. Triangle Congruence Theorems List the “shortcuts” for all of the theorems that can be used to prove triangle congruence. _______________________________________________________. 16. Isosceles Triangle Theorem (and it’s Converse) If two sides of a triangle are congruent, then _______________________________________ ____________________________________________________________. If two angles of a triangle are congruent, then ______________________________________ ____________________________________________________________. If a triangle is equilateral, then it is _________________________________. If a triangle is equiangular, then it is _________________________________. 17. Triangle Midsegment Theorem A midsegment of a triangle is ______________________ to a side of the triangle, and it’s ___________________ is ________________ the length of that side. 18. Triangle Inequality Theorem The _____________ of any two sides of a triangle must be ____________________________ ___________________________________________________________________. 19. Pythagorean Inequalities Theorem In ABC, c is the length of the longest side. If __________________________, then ABC is an obtuse triangle. If _____________________________, then ABC is an acute triangle. 20. 45° -45° – 90° Triangle Theorem In a 45 – 45 – 90 triangle, both legs are ________________________, and the length of the hypotenuse is the length of the leg times ___________. 21. 30° – 60° – 90° Triangle Theorem In a 30 – 60 – 90 triangle, the length of the hypotenuse is ________ times the length of ________________________________, and the length of the longer leg is the length of the shorter leg times __________. Vocabulary You Should Know! Coplanar Collinear Ray Opposite Rays Midpoint Bisect Segment Bisector Acute Right Obtuse Angle Bisector Congruent Adjacent Angles Linear Pair Complementary Supplementary Vertical Angles Hypotenuse Conjecture Counterexample Inductive Reasoning Deductive Reasoning Conditional Statement Converse Inverse Contrapositive Alternate Exterior Angles Alternate Interior Angles Corresponding Angles Distance From a Point To A Line Parallel Lines Perpendicular Bisector Skew Lines Transversal Same – Side Interior Angles Corresponding Angles / Sides Median Equiangular Equilateral Scalene Triangle Vertex Angle Remote Interior Angle Obtuse Triangle Isosceles Triangle Altitude Pythagorean Triple Midsegment of a Triangle Formulas You Should Be Familiar With! Slope Formula: y2 y1 x2 x1 Distance Formula: Midpoint Formula: x1 x2 y1 y2 , 2 2 x2 x1 2 y2 y1 2 Slope – Intercept Form of a Line: y mx b Point – Slope Form of a Line: y y1 mx x1 30 – 60 – 90 Triangles: 45 – 45 – 90 Triangles: x , x 3 , 2x x, x,x 2