Semester 1 Final Exam Review

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1 Target 1: Vocabulary and notation Semester 1 Final Exam Review Name 1. Find the intersection of MN and LO. 2. 3) Vocabulary: Define the following terms and draw a diagram to match: a) Point b) Line c) Plane d) Ray e) Opposite Ray f) Parallel Lines g) Perpendicular Lines h) Acute Angles i) Obtuse Angles j) Right Angles k) Straight Angles l) Adjacent Angles m) Coplanar n) Collinear Target 2: Segment/Angle Addition Postulate 4) 5)

2 Target 3: Translations 7. Given quadrilateral S (1, 2), H (3, 1), O (4, -1), P (2, 0), translate it according to the rule (x, y) (x + 4, y -2). What are the coordinates of the image? S H 8. Write the rule that translates the preimage to the image. O P 9. The point Z (2, -3) is the image under the translation (x, y) (x + 3, y - 2). What is the preimage? Z (, ) Target 4: Reflections Patty performed a reflection across line m. Did she do it correctly? If yes, use correct mathematical vocabulary to convince me she did. If no, use correct mathematical vocabulary to tell me she did not. 12. Write the rule that describes the transformation.

3 Target 5: Naming Angle Pairs 13) Given a b cut by a transversal c, which of the following statements is not true. A) 1 and 3 are corresponding angles B) 2 and 3 are same-side int. angles C) 3 and 4 are vertical angles D) 1 and 4 are alternate int. angles 14) Refer to the diagram. A) Name a pair of same-side interior angles. B) Name a pair of corresponding angles. C) Name a pair of alternate interior angles. Target 6: Rotations 15. Rotate the figure 90 CCW about the origin. 16. Rotate the figure 90 CW about point C. 17. Rotate the figure 90 CCW about the point (2, 3) Target 7: Symmetry 18. Given a regular 4-sided polygon (also known as a square), answer the following questions: a. How many lines of symmetry does it have? b. Does it have point symmetry? c. What is the minimum number of degrees it will take to rotate the figure onto itself? Target 8: Compositions 19. Reflecting an object in two parallel lines will result in a (pick 1) a. reflection b. translation c. rotation d. dilation

4 20. Reflecting an object in two intersecting lines will result in a (pick 1) a. reflection b. translation c. rotation d. dilation 21. Graph the figure B(-3, -2), A(-4, -4), T(-2, -4) then perform the glide reflection according to the rules (x, y) (x -3, y) and reflect across y = -4. Target 9: Slope Determine whether the pair of lines is parallel, perpendicular, or neither x + 3y = x + 3y = x + 3y = 7 y = -3/2x 4 y = 3/2x 4-2x-3y = -1 Target 10: I can write the equation of a line. (Pick either form) 25. Write the equation of the line through the points (-1, 3) and (0, 4) 26. Write the equation of the line in slope intercept form parallel to 3y = -x + 2 through the point (-3, -2). 27. Write the equation of the line in point-slope form perpendicular to y = 2x - 2 through the point (-2, 3).

5 Target 11: Angle pairs with algebra 28. Find the measure of the numbered angles. m 1 = m 1 = m 1 = m 1 = m 2 = m 3 = m 4 = 29. Find x Target 12: Proofs with parallel lines 30. Using transformations, show that a b 31. Given a b cut by a transversal c, which of the following statements are not true. A) 1 3 B) 2 3 C) 3 4 D) 1 4

6 Target 13: Dilations 32. Dilate the cow by a scale factor of 3 centered at the origin. 33. Dilate the cow by a scale factor of ½ centered at (2, 1). C ( -2, 0) O (0, 2) W (2, 0) C(-2, 1) O (-4, 3) W (-2, 5) 34. Is ΔE F G a dilation of ΔEFG? Claim: Evidence: Segment Slope Length Conclusion: Is ΔE F G a dilation of ΔEFG? Reasoning (Use specific examples from your evidence):

7 Target 14: Similar polygons with algebra 35) The two rectangles are similar. Which is a correct proportion for corresponding sides? 4 m 12 m 8 m a. b. c. d. x 36) The skyscraper in Chicago is 1450 feet high. A model of the skyscraper is 24 inches tall. What is the ratio of the height of the model to the height of the actual skyscraper? 37) Solve the proportion. 38) The figures are similar. Give the ratio of the perimeters and the ratio of the areas of the first figure to the second. The figures are not drawn to scale ) Find the ratio of the perimeter of the larger rectangle to the perimeter of the smaller rectangle. 5 ft 3 ft 9 ft 11 ft 40) You want to produce a scale drawing of your living room, which is 24 ft by 15 ft. If you use a scale of 4 in. = 6 ft, what will be the dimensions of your scale drawing?

8 41) Figure. Name a pair of corresponding sides? 42) ABCD ~ WXYZ. AD = 6, DC = 3, and WZ = 59. Find ZY. The figures are not drawn to scale. 43) Triangles ABC and DEF are similar. Find the lengths of AB and EF. A D 5x 5 E x F B 4 C 44) Campsites F and G are on opposite sides of a lake. A survey crew made the measurements shown on the diagram. What is the distance between the two campsites? The diagram is not to scale. 45) Find x and y, given that. A 8 P Q x 18 B y C

9 46) Find the value of the variable(s). If your answer is not an integer, leave it in simplest radical form. x y Not drawn to scale Target 15: Proving triangles are similar State whether the triangles are similar. If so, write a similarity statement, the similarity ratio and the postulate or theorem you used. 47) a. b. In ABC, AB = 8, AC = 10 and A = 24 o. In DEF, DE = 12, DF = 15 and D = 24 o. Similar? Similarity Statement Reason Similar? Similarity Statement Reason Target 16: SOH CAH TOA/Pythagorean Theorem/Right Triangle stuff 48) Find the length of the missing side. The triangle is not drawn to scale ) Write the tangent ratios for and. P R 20 Q Not drawn to scale

10 50) Find the value of x. Round to the nearest tenth. 10 x Not drawn to scale 51) MK is the bisector of AB. Find the value of each variable. (not drawn to scale) Target 17: Angles of elevation and angles of depression 52) A large totem pole in the state of Washington is 100 feet tall. At a particular time of day, the totem pole casts a 249- foot-long shadow. Find the angle of elevation to the nearest degree. 53) A spotlight is mounted on a wall 7.4 feet above a security desk in an office building. It is used to light an entrance door 9.3 feet from the desk. To the nearest degree, what is the angle of depression from the spotlight to the entrance door? Target 19: Properties of congruency 54) If DLQ EMR, then which of the following are not true? A) LDQ MRE B) DLQ EMR C) RME QLD D) MRE LQD 55) XYZ ABC. What angle is congruent to Y?

11 Target 20: Proving triangles are congruent 56) State the postulate or theorem you can use to prove the triangles congruent. If the triangles cannot be proven congruent, write not possible. 57) Name a pair of overlapping congruent triangles. State whether the triangles are congruent by SSS, SAS, ASA, AAS, or HL. 58) Which two sides must be congruent to use ASA to prove DMX JCX? 59) Which two angles must be congruent to use SAS to prove ADX CBX? 60) Are the triangles congruent? If so, write a congruence statement and justify your reasoning. If not, write not congruent.

12 61) Given: AB DC AD BC Prove: ADC CBA 62) Given: EI and HF bisect each other at G. Prove: E I 63) Given: MJ JK KL ML JK ML Prove: JM KL

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