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Geometry Test Theorems, Definitions, and Proofs Review Name: _________________________________ Part One: Vocabulary 1. In an _________________________ we are given the hypothesis, and trying to prove the conclusion. 2. _________________________ is an argument that recognizes patterns in experiments or specific examples to draw conclusions. 3. _________________________ is an argument that uses known facts in order to prove conclusions. 4. A line that crosses at least two other lines is called a ___________________________. 5. a) In the diagram to the right, angles 1 and 2 are a __________________________________. b) List a different pair of angles that also fit this description. 6. a) In the diagram to the right, angles 5 and 7 are ____________________________________. b) List a different pair of angles that also fit this description. 7. a) In the diagram to the right, angles 2 and 6 are ____________________________________. b) List a different pair of angles that also fit this description. 8. a) In the diagram to the right, angles 2 and 8 are ______________________________________. b) List a different pair of angles that also fit this description. 9. a) In the diagram above, angles 4 and 6 are ____________________________________. b) List a different pair of angles that also fit this description. 10. a) In the diagram to the right, angles 3 and 6 are ___________________________________. b) List a different pair of angles that also fit this description 11. a) In the diagram above, angles 1 and 8 are ______________________________________. b) List a different pair of angles that also fit this description. 12. Angles whose measures add together to give us 180 degrees are called _______________________. 13. Shapes are __________________ if corresponding angle measures are congruent and corresponding sides have equal ratios. 14. Shapes are __________________ if corresponding angle measures are congruent and corresponding sides are congruent. 15. The ratios of corresponding sides of similar figures are called the ____________________. 16. A line that cuts a line segment in half at a 90 degree angle is called a ________________________. 17. A line that cuts an angle in half is called an _____________________. 18. The line that connects the midpoint of a triangleβs side to its opposite vertex is called a _______________________. 19. Perpendicular bisectors of a triangle are _________________________. 20. The point where all three perpendicular bisectors of a triangle meet is called the ____________________ which is the center of a _________________________ circle. 21. The point where all three angle bisectors of a triangle meet is called the __________________ which is the center of an __________________________ circle. 22. The point where the medians of the triangle intersect is called the ____________________ which is the center of gravity for the triangle. 23. A four sided figure is called a ____________________. 24. A quadrilateral that has exactly one pair of parallel sides must be a ________________________. 25. A parallelogram has opposite sides which are ____________________ and _____________________. 26. A ____________________ is a quadrilateral with two pairs of consecutive congruent sides. 27. A quadrilateral with four congruent sides and four right angles is called a ____________________. 28. A quadrilateral with four congruent sides and no right angles is called a ____________________. 27. A parallelogram with right angles and two different side measures in called a ________________________. Part Two: For each of the following theorems or postulates fill in the blank, then draw and label a diagram to represent the theorem. 28. Parallel Lines Postulate: Two lines cut by a transversal are parallel if and only if ________________________ have equal measure. Diagram: 29. Linear Pairs Postulate: If two angles are a linear pair, then the sum of their measures is ____________. Diagram: 30. Vertical Angle Theorem: If two angles are vertical angels, then their measures are__________________. Diagram: 31. Alternate Exterior Angle Theorem: Two lines cut by a transversal are ______________ if and only if alternate exterior angles are congruent. Diagram: 32. ____________________________: Two lines cut by a transversal are parallel if and only if same side exterior angles are supplementary. Diagram: 33. Alternate Interior Angle Theorem: Two lines cut by a transversal are parallel if and only if alternate interior angles are ______________________. Diagram: 34. Same Side Interior Angle Theorem: Two lines cut by a transversal are parallel if and only if same side interior angles are _____________________________ Diagram: 35. ________________________ Theorem: the exterior angle of a triangle has a measure equal to the sum of the measures of the two remote interior angles. Diagram: 36. Angle Addition Postulate: If P is a point in the interior of β π΄π΅πΆ, then πβ π΄π΅π + πβ ππ΅πΆ = _________________. Diagram: Μ Μ Μ Μ 37. _____________________________: If P is a point on segment π΄π΅ then π΄π + ππ΅ = π΄π΅. Diagram: 38. Side-Angle-Side Similarity Theorem: If the angle of one triangle has the same measure as an angle of a second triangle, and the lengths of corresponding sides including these angles are multiplied by the same scale factor then the two triangles are ___________________. Diagram: 39. Angle-Angle Similarity Theorem: If the measure of two ________of one triangle are the same as the measures of two _________of another triangle then the two triangles are similar. Diagram: 40. Side-Side-Side Similarity Theorem: If the lengths of the three side of one triangle are multiplied by the same ______________ to obtain the length of the three sides of another triangle , then the two triangles are similar. Diagram: 41. Hypotenuse-Leg Theorem: The hypotenuse leg theorem states that any two _________ triangles that have a congruent hypotenuse and a corresponding congruent leg are congruent triangles. Diagram: 42. Midpoint Connector Theorem for Triangles: If a line segment joins the midpoints of two sides of a triangle, then it is _______________to and ____________the length of the third side. Diagram: 43. Triangle Proportionality Theorem: If a line parallel to one side of a triangle intersects the other two sides of the triangle, then the line divides these two sides _________________. Diagram: 44. Midpoint Connector Theorem for Quadrilaterals: If the midpoints of consecutive sides of any quadrilateral are connected, the resulting quadrilateral is a________________. Diagram: 45. Organize the following conditions into the section(s) they belong: SSS; SAS; SSA; ASA; AAS; AA; Hypotenuse-Leg Similarity Congruence Not enough information to show similarity or congruence Part Three: Label each of the following diagrams using color to show every piece of information we know. Ignore the place that says proof until you get to part four. 46. Given: AS bisects οHAG; οH ο οG Proof: B 47. Given: BF ο ON ; BF || ON O R Proof: F N 48. Given: AN ο NL; LG ο GE ; οGNL ο οNGL; L is the midpoint of AE N Proof: A G L E 49. Given: GM ο WH , MAοAG , MA ο HO , HOοWO Proof: Part Four: For each of the diagrams above that you have labeled prove the following in the space provided above. Μ Μ Μ Μ β πΊπ Μ Μ Μ Μ For #46 prove π»π For #47 prove R is the midpoint of Μ Μ Μ Μ π΅π For #48 prove β π΄ β β πΈ For #49 prove βπΊπ΄π β βπππ»