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Geometry Final Honors Geometry Name: _____________________________________ Semester 1 Final Exam Review For numbers 1 – 4, use the diagram. 1. Name two pairs of numbered angles that are supplementary. 2. Name two pairs of numbered angles that are complementary. 3. Name a pair of numbered angles that are vertical. 4. How many angles have their vertex at D? 5. Find the value of x. 6. Find the value of x. 7. The measure of the supplement of an angle exceeds three times the measure of the complement of the angle by 12. Find the measure of half of the supplement. 8. ABCD is a rectangle. Find the coordinates of P, the midpoint of .AC 9. The measure of the supplement of an angle is 82 more than five times the measure of the complement of the angle. Find the measure of the complement. 10. Find the area of the rectangle whose vertices are (–6, 7), (–15, –2), (–6, –2), and (–15, 7) y B(18, 12) C D A P . D F C B A 5 4 3 2 132° x° 130° 50° x° TakeHomeFinal x° 11. In this figure, lines a, b, c, d, e, and f intersect as shown. Based on the angle measures, which pair of lines is parallel? a) a and c b) c and b c) d and e d) a and b 12. The ratio of m A : m B m C of ∆ABC is 4 : 9 : 5 . Find the measure of the smallest angle. 13. Find the value of x. 14. The slope of a line is 5 3 . The line contains the point (–8, 10) and a point whose x coordinate is 7. Find the y-coordinate of that point. 15. For which two lines are 1 and 2 a pair of alternate interior angles? 16. If ABC and ECD are corresponding angles, which line is the transversal? 17. Find the angle formed by the hands of a clock at 1:45. 18. One side of a rectangle is 18 and the perimeter is 48. What is the area? 19. If the legs of an isosceles triangle andPQ TP , name the base. F K J H 1 2 A B C E D a b c e d 137° 33° 33° 137° 20. The sides of a rectangle are in a ratio of 5:7 and the perimeter is 72. Find the area of the rectangle 21. ΔABC ΔDEF, DF = 10, AB = 18, and the perimeter of ΔABC is 40. Find DE + EF. 22. If the sides of a triangle are 6, 8, and x, find the range of possible values for x. 23. Given ABC ACB, BD bisects ABC, CD bisects ACB, give the reason for the conclusion of 3 4. 24. Write a valid inequality of the restrictions on x. 25. Write a valid inequality of the restrictions on x. 26. Find the restrictions on the value of x. 27. ΔABC is a right triangle with PQ < qr. what is a possible measure from r? 28. in the figure, lines a and b are intersected by line t and 2 3. why are lines a and b are parallel? b a c d 3 1 2 4 20° (6x – 10)° (4x)° (6x – 20)° 4 2x+ 34 3 p r q 29. write an equation of a line that is perpendicular to line l on the graph to the right. 30. what is the midpoint of the segment joining (2, 6) and (10, 12)? 31. which figure contains two congruent triangles? a) b) c) d) 32. in the diagram below, quadrilateral pqrs is congruent to quadrilateral twvu. list all pairs of congruent sides. 33. fill in the reasons for the proof below. statements reasons 1. parallelogram abcd 1 2 1. given 2. b d 2. 3. ab dc 3. 4. ∆abx ∆cdy 4. 5. bx dy 5. 34. in the figure below, ∆xyz ∆xwz. what is the length of ?xy qr.="" what="" is="" a="" possible="" measure="" from="" r?="" 28.="" in="" the="" figure,="" lines="" a="" and="" b="" are="" intersected="" by="" line="" t="" and="" 2="" 3.="" why="" are="" lines="" a="" and="" b="" are="" parallel?="" b="" a="" c="" d="" 3="" 1="" 2="" 4="" 20°="" (6x="" –="" 10)°="" (4x)°="" (6x="" –="" 20)°="" 4="" 2x+="" 34="" 3="" p="" r="" q="" 29.="" write="" an="" equation="" of="" a="" line="" that="" is="" perpendicular="" to="" line="" l="" on="" the="" graph="" to="" the="" right.="" 30.="" what="" is="" the="" midpoint="" of="" the="" segment="" joining="" (2,="" 6)="" and="" (10,="" 12)?="" 31.="" which="" figure="" contains="" two="" congruent="" triangles?="" a)="" b)="" c)="" d)="" 32.="" in="" the="" diagram="" below,="" quadrilateral="" pqrs="" is="" congruent="" to="" quadrilateral="" twvu.="" list="" all="" pairs="" of="" congruent="" sides.="" 33.="" fill="" in="" the="" reasons="" for="" the="" proof="" below.="" statements="" reasons="" 1.="" parallelogram="" abcd="" 1="" 2="" 1.="" given="" 2.="" b="" d="" 2.="" 3.="" ab="" dc="" 3.="" 4.="" ∆abx="" ∆cdy="" 4.="" 5.="" bx="" dy="" 5.="" 34.="" in="" the="" figure="" below,="" ∆xyz="" ∆xwz.="" what="" is="" the="" length="" of="">