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GEOMETRY – FIRST SEMESTER EXAM REVIEW VOCABULARY: You need to know (and understand) the formal definitions of these terms. You will need to know them to answer multiple choice questions and solve problems on the written part of the test. 1. 2. 3. 4. 5. 6. 7. Equilateral Triangle Equiangular Triangle Acute Triangle Scalene Triangle Obtuse Triangle Right Triangle Isosceles Triangle 8. Perpendicular Bisector 9. Angle Bisector 10. Median 11. Altitude of a Triangle 12. Centroid 13. Circumcenter 14. Incenter 15. Orthocenter 16. Parallelogram 17. Rectangle 18. Rhombus 19. Square 20. Trapezoid 21. Isosceles Trapezoid 22. Vertical Angles 23. Linear Pair 24. Alternate Interior Angles 25. Corresponding Angles 26. Consecutive Interior Angles 27. Alternate Exterior Angles 28. Conditional Statement 29. Converse 30. Inverse 31. Contrapositive 32. Hypothesis of a conditional 33. Conclusion of a conditional 34. Complementary Angles 35. Supplementary Angles 36. Regular Polygon 37. Parallel Lines 38. Skew Lines 39. Parallel Planes FORMULAS – These are formulas you should have memorized and be able to use on the exam when necessary. 1. Distance 2. Midpoint 3. Slope 4. Sum of the measures of the interior angles of a polygon 5. Measure of each interior angle of a regular polygon 6. Sum of the measures of the exterior angles of a polygon 7. Measure of each exterior angle of a regular polygon POSTULATES, PROPERTIES AND THEOREMS 1. All the postulates from section 2-5 (page 127) – Used for sometimes/always never 2. All the properties from section 2-6 (page 136) 3. Segment Addition Postulate 4. Angle Addition Postulate 5. Vertical Angle Theorem 6. Corresponding Angle Postulate 7. Alternate Interior Angle Theorem 8. Consecutive Interior Angle Theorem 9. Alternate Exterior Angle Theorem 10. Triangle-Angle Sum Theorem 11. Exterior Angle Theorem 12. SSS 13. SAS 14. ASA 15. AAS 16. Perpendicular Bisector Theorem 17. Circumcenter Theorem 18. Angle Bisector Theorem 19. Incenter Theorem 20. Centroid Theorem 21. Reminder to study the chart on page 339!!! 22. Exterior Angle Inequality Theorem 23. Angle-Side Relationships in Triangles (pg 346) 24. Triangle Inequality Theorem 25. Hinge Theorem 26. Properties of Parallelograms (pg 403-405) 27. Properties of Rectangles (pg 423) 28. Properties of a Rhombus (pg 430) 29. Properties of a Square 30. Properties of Trapezoids and Isosceles Trapezoids PRACTICE PROBLEMS – The rest of this review is made up of practice problems similar to what you will see on the exam in either the multiple choice or the written portion. 1. Classify the following pairs of angles using the diagram below. Remember that “none” is an option. a. 9 and 13 _______________________ b. 1 and 11 _______________________ c. 5 and 6 _______________________ d. 3 and 13 _______________________ e. 7 and 13 _______________________ f. 3 and 8 _______________________ g. 1 and 3 _______________________ 2. Use the diagram to the right to determine which lines, if any, must be parallel given the information below. a. 10 = 2 _________________________ b. 11 = 13 __________________________ c. 5 + 12 =180 _________________________ d. 1 = 3 _______________________________ 3. Write the converse, inverse and contrapositive of the following statement: If two angles are supplementary, then their measures add to 180 degrees a. Converse: __________________________________________________________________ b. Inverse: ____________________________________________________________________ c. Contrapositive: _______________________________________________________________ 4. Use the statement below to identify the hypothesis and the conclusion: If 2x – 5 = 11, then x = 8 Hypothesis: _______________________________ Conclusion: _______________________________ 5. List what postulate or theorem could be used to prove the triangles congruent and then write the congruence statement. a. b. _________________ ________________ _________________ _________________ 6. Find the sum of the measures of the interior angles of a convex 22-gon. 7. Find the sum of the measures of the exterior angles of a decagon. 8. Find the distance between the two points A (-3, -7) and B (4, 3). 9. Find the midpoint of a segment with the endpoints X(10, -4) and Y(-3, 9). For 10-11 use the figure at the right. ⃗⃗⃗⃗ . 10. If m RTS = 8x + 18, find the value of x so that ⃗⃗⃗⃗⃗ TR TS 11. If m PTQ = 3y –10 and m QTR = y, find the value of y so that PTR is a right angle. 12. Construct a truth table for the statement (4 points) ~p v (q ᴧ r) For 13-15, find the measure of each numbered angle using the diagrams and information below. 13. 14. m∠7 = 5x + 5, m∠8 = x – 5 15. ∠9 and ∠10 are complementary ∠7 ≅ ∠9, m∠8 = 41 m∠11 = 11x, m∠13 = 10x + 12 16. Find X and Y. X: ___________________ Y: ___________________ 17. In the diagram below m 2 = 96 and m 12 = 103. Find the measures of the angles below. a. 9 ____________ b. 10 _____________ c. 5 ______________ d. 11 _____________ e. 13 ______________ f. 8 _______________ For 18 and 19, write the equation of each line in slope-intercept form with the given information. 18. m=- 3 and through point (-4, 6) 2 19. Through points (-4, 2) and (8, -1) For 20 and 21, use the diagram to classify the given triangles by SIDES. 20. 21. For 22 and 23, use the diagram to classify the triangles by ANGLES. 22. XUZ ______________ 23. UYX __________________ 24. In △MIV, Z is the centroid, MZ = 4, YI = 21, and NZ = 3. Find each measure. A) ZR __________ B) YZ __________ C) MR __________ D) ZV __________ E) NV __________ F) IZ __________ 25. Point A is the incenter of △PQR. Find each measure. A) m ARU _______________ B) AU _______________ C) m QPK _______________ 26. Is it possible to form a triangle with side lengths of 12, 13, 14? If not, explain why not. 27. Is it possible to form a triangle with side lengths of 20, 43, 22? If not, explain why not. 28. Find the range of the measures of the third side of the triangle given that the other two sides are 32cm and 150cm. For 29 and 30, use an inequality to compare the given measures. 29. m∠ STR and m∠ TRU _________________ 30. PQ and RQ ________________ For 31 and 32 use RECTANGLE RSTU. Circle your answer. 31. If UZ = 3x - 5 and ZS = 2x + 11, find US. 32. If m∠SUT = 2x - 7 and m∠RUS = 2x + 5, find m∠SUT. For 33-35, use RHOMBUS DKLM. Circle your answer. 33. If m∠DML = 78 find m∠DKM. 34. If m∠KAL = 3x - 15, find x. 35. If DA = 3x - 1 and AL = x + 9, find DL. PROOF REVIEW Do all your proofs on a separate sheet of paper. These should be two-column proofs 1. Given: 4𝑥 + 6 2 =9 Prove: x = 3 2. Given: −5(𝑥 + 4) = 70 Prove: x = -18 3. Given: 1 4 AND 2 3 Prove: AFC = EFC 4. Given: X is the midpoint of WY and VZ Prove: VW = ZY 5. Given: m∠1 + m∠3 = 180 Prove: ∠2 ≅ ∠3 6. Given: AB = DE and BC = EF Prove: AC = DF 7. 8. Given: 𝑟 ∥ 𝑠 Prove:∠1 is supplementary to ∠6 9. Given: ∠1 ≅ ∠2, ∠1 ≅ ∠3 ̅̅̅̅ ∥ ̅̅̅̅ Prove: 𝑨𝑩 𝑫𝑪 10. 11. Given: ∠S ≅ ∠V, T is the midpoint of ̅̅̅̅ 𝑆𝑉. Prove: △RTS ≅ △UTV 12. 13. Given: ∠D ≅ ∠F ̅̅̅̅ 𝐺𝐸 bisects ∠DEF. Prove: ̅̅̅̅ 𝐷𝐺 ≅ ̅̅̅̅ 𝐹𝐺 14. 15. For 16 and 17, write an INDIRECT PROOF. Makes sure to include all the steps of an indirect proof. 16. Given: -4x + 2 < -10 Prove: x > 3 17. Given: 5x – 2 < 13 Prove: x < 3