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1 Geometry Semester 1 Final Review Chapter 1 Study Guide Vocab: define in your own words Adjacent angles Angle bisector Name_______________________ Complementary angles Supplementary angles Congruent Linear pair Opposite Rays Midpoint 1. Y is between X and Z. XY = 13.8, and XZ = 21.4. Find YZ (sketch it). 2. U is the midpoint of ̅̅̅̅ TV, TU=3x+4 and UV = 5x-2. Find TU, UV, and TV (sketch it). 3. Classify each of the five possible angles as acute, right, or obtuse. 4. ⃗⃗⃗⃗⃗⃗ 𝑁𝑃 bisects ∠𝑀𝑁𝑄, m∠𝑀𝑁𝑃 = (6𝑥 − 12)˚, and 𝑚∠𝑃𝑁𝑄 = (4𝑥 + 8)˚. a. Draw a sketch of the angles b. Find 𝑚∠𝑀𝑁𝑄. 5. Tell whether the angles are only adjacent, adjacent and form a linear pair, or not adjacent. a. ∠1 𝑎𝑛𝑑 ∠2 b. ∠3 𝑎𝑛𝑑 ∠4 c. ∠2 𝑎𝑛𝑑 ∠5 6. Find the measure of the complement and the supplement of each angle a. 7. Find the midpoint of ̅̅̅̅ 𝐴𝐵 with A(3,2) and B(-1, 4). b. X=18 2 ̅̅̅̅ with Q(-8,-5) and R(-4,7). 8. Find the midpoint of 𝑄𝑅 9. Use the Pythagorean Thm or the distance formula to find the distance between X(3,-5) and Y(8,4). 10. Use the Pythagorean Thm or the distance formula to find the distance between X(-2,4) and Y(6,1). Constructions Study Guide 1. Copy ̅̅̅̅ 𝑅𝑆 ̅̅̅̅: 4. Perpendicularly bisect 𝑈𝑉 List the steps: 2. Copy ∠𝑇𝑅𝑆. List the steps: 3. Construct a triangle congruent to ∆RTS. 5. Construct an angle bisector for ∆RTS at ∠𝑇𝑅𝑆. List the steps: 3 Chapter 3 Study Guide Vocab: define in your own words 1. Transversal Alternate exterior angles Alternate interior angles Corresponding angles Corresponding sides Parallel lines Perpendicular lines Point-slope form (linear equation) Identify the transversal and classify each angle pair: a. ∠5 𝑎𝑛𝑑 ∠2 b. ∠6 𝑎𝑛𝑑 ∠3 c. ∠2 𝑎𝑛𝑑 ∠4 d. ∠1 𝑎𝑛𝑑 ∠2 2. Find 𝑚∠𝐷𝐸𝐹 3. Find 𝑚∠𝐴𝐵𝐶 4. Find 𝑚∠𝐾𝐿𝑀 5. Find 𝑚∠𝑄𝑅𝑆 Write the equation of each line in slope-intercept form. 6. 7. 8. Same-side interior angles Slope Slope-intercept form (linear equation) 4 Write the equation of each line in the given form. 2 9. The line with slope − 3 through (3, -1) in point-slope form. 10. The line through (-2, 2) and (4,-1) in slope-intercept form. Use slopes to determine if the lines are parallel, perpendicular, or neither. ⃡⃗⃗⃗⃗ 11. 𝐸𝐹 𝑎𝑛𝑑 ⃡⃗⃗⃗⃗ 𝐺𝐻 for E(8,2), F(-3, 4), G(6, 1), and H(-4, 3) 12. ⃡⃗⃗⃗ 𝐽𝐾 𝑎𝑛𝑑 ⃡⃗⃗⃗⃗ 𝐿𝑀 for J(4,3), K(-4, -2), L(5,6), and M(-3, 1) 13. What is the equation in slope-intercept form of the line parallel to y=-3x+4 that goes through the point (5,-2)? 3 14. What is the equation in slope intercept form of the line parallel to 𝑦 = 4 𝑥 − 6 that goes through the point (-8, 2)? 15. What is the equation in slope-intercept form of the line perpendicular to y=5x-7 that goes through the point (10, 6)? 4 16 What is the equation in slope-intercept form of the line perpendicular to 𝑦 = − 7 𝑥 − 6 that goes through the point (8, -3)? 5 Chapter 12 Study Guide Vocab: define in your own words Transformation Image and Pre-Image Translation Reflection Glide reflection Line of symmetry Reflection Rotational symmetry 1. Use the translation (𝑥, 𝑦) → (𝑥 + 3, 𝑌 − 3). Find the new set of coordinates and sketch. 2. Reflect the figure with the given vertices across the given line. a. E(-3, 2), F(0,2), G(-2, 5); reflect across xaxis. b. P(6,4), Q(9, 4), and R(9,1); reflect across y = x. 3. Translate the figure with the given vertices along the given vector. a. R(1, -1), S(1, -3), T(4, -3), U(4, -1); translate {-5, 2}. b. M(1, 4), N(4,4), P(3,1); translate {3, 3}. 6 4. Using the diagram below, reflect quadrilateral ABCD over the line y = x. Label the vertices of the image. 5. Using the diagram to the right describe the rotation that carries MATH onto M’A’T’H’. ___________degrees clockwise/counterclockwise (circle one) 6. Using the diagram to the right, write a rule for the translation of ABCD to A’B’C’D’. (𝑥, 𝑦) → (_______ , ________) 7. Tell if each figure below has rotational symmetry. If so, state the angle of rotational symmetry and the order of symmetry. a. b. 7 Chapter 4 Study Guide Vocab: define in your own words Acute triangle Base angle CPCTC Exterior angle Interior angle Isosceles triangle Equilateral Obtuse triangle Right triangle Equiangular Scalene triangle 1. Find 𝑚∠𝑁 using the figure at right. 2. In ∆LMN, 𝑚∠𝐿 = 8𝑥˚, 𝑚∠𝑀 = (2𝑥 + 1)˚, 𝑎𝑛𝑑 𝑚∠𝑁 = (6𝑥 − 1)˚. a. Sketch the triangle b. Find 𝑚∠𝑁 3. ∆ABC ≅ ∆CDA a. find x b. find CD 4. Name all the 5 ways two triangles can be proven congruent. Choose two and draw an example of each. 4. Given: 𝑚 ∥ l, and 𝑚∠𝐿𝑀𝐾 = 60° Prove: m∠𝐺𝐹𝐻 = 120° 5. 8 ̅̅̅̅ ∥ 𝑄𝑃 ̅̅̅̅ 𝑎𝑛𝑑 𝑁𝑂 ̅̅̅̅ ≅ 𝑄𝑃 ̅̅̅̅ 6. Given: 𝑁𝑂 ̅̅̅̅ ̅̅̅̅ Prove: 𝑁𝑄 ≅ 𝑂𝑃 7. ∠𝑊 ≅ ∠𝑌 ̅̅̅̅. 9. Find 𝑅𝑆 8. Find 𝑚∠𝐵 given 𝑚∠𝐴 = 3𝑡 and 𝑚∠𝐶 = 2𝑡 + 19 Chapter 5 Study Guide Vocab: define in your own words altitude of a triangle median of a triangle midsegment of a triangle 1. In ∆XYZ, find each measure a. BC b. XZ c. 𝑚∠𝑌𝑋𝑍 d. 𝑚∠𝐵𝐶𝑍 2. Classify each triangle according to its side lengths and angle measures. a. 9, 12, 16 b. 1.5, 3.6, 3.9 c. 3.7, 3.7, 4.1 9 3. Find the value of x. Give your answer in the simplest radical form. a. b. x c. 4. A triangle has vertices A(11, 0), B(13, 12), and C(4,4). Find the equation of the ̅̅̅̅ . median from vertex B to 𝐴𝐶 Chapter 6 Study Guide Know the properties/conditions for each: Quadrilateral Parallelogram Rectangle Rhombus Square Trapezoid 1. Read each statement, then circle always, sometimes, or never true. a. A rectangle is a rhombus. Always Sometimes Never b. A trapezoid is a parallelogram Always Sometimes Never 2. LKMN has coordinates L(-5,3), K(1,1), M(0,-2), and N(-6,0). Determine if it is any of the following: a parallelogram, a rectangle, a rhombus, and/or a square.