College Prep Geometry MIDTERM STUDY GUIDE. Mrs. Miller. Name: Due: Thursday, January 9, 2014


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1 College Prep Geometry MIDTERM STUDY GUIDE Mrs. Miller Name: Due: Thursday, January 9, 04 To receive full credit you must have Tried EVERY PROBLEM Work shown for EVERY PROBLEM All work done in this packet
2 Class: Date: CP Geometry Midterm Exam Study Guide Short Answer Refer to Figure. Figure. Name the intersection of lines m and n.. Name a line that contains point G. 3. Name the plane containing lines p and m. 4. What is another name for line p?
3 5. Name three points that are collinear. Refer to Figure. Figure 6. How many planes are shown in the figure? 7. Name the intersection of plane DAB and a plane EBC.
4 Refer to the figure below. 8. Name all segments parallel to AB. 9. Name all segments skew to GH. Find the measurement of the segment. 0. PR = 6.3 mm, RS =. mm PS =? Use the number line to find the measure.. RH 3
5 Use the Distance Formula to find the distance between each pair of points.. Find the coordinates of the midpoint of a segment having the given endpoints. 3. QÊ Ë Á, 8 ˆ, R Ê Ë Á, ˆ In the figure, GK bisects FGH. 4. If m FGK = 6v 3 and m KGH = 3v + 6, find angle x. 4
6 5. The measures of two complementary angles are 8q 5 and 8q + 5. Find the measures of the angles. Make a conjecture about the next item in the sequence. 6., 8, 7, 6, In the figure, m NML = 35, PQ Ä TU and KL Ä NM. Find the measure of angle TLR. 8. In the figure, AB Ä CD. Find x and y. 5
7 Write the statement in ifthen form. 9. Two angles measuring80 are supplementary. 0. Identify the hypothesis of the statement Two angles are complementary if they have a sum of 90 degrees... Identify the conclusion of the statement Two angles are complementary if they have a sum of 90 degrees.. Determine whether the conjecture is true or false. Give a counterexample for any false conjecture.. Given: m + 6 = 5 Conjecture: m = 3 3. Given: Two angles are adjacent. Conjecture: They are both acute angles. 6
8 Use the figure to find the angles. 4. Name two acute vertical angles and two obtuse vertical angles. Obtuse: Acute: Explain the difference between the two answers. 5. Name a linear pair. 7
9 Given the following information, determine which lines are parallel. State the postulate or theorem that justifies your answer. (Correspondong, Alternate interior/exterior, Consecutive interior/exterior, Vertical, Linear Pair) In the figure, p Ä q. Find m. 8
10 Write an equation in pointslope form of the line having the given slope that contains the given point. 8. m = 3, Ê Ë Á, ˆ Find each measure. 9. m, m, m m, m, m 3 9
11 Identify the congruent triangles in the figure. 3. Name the congruent angles and sides for the pair of congruent triangles. 3. GHK XZT 33. Triangle FJH is an equilateral triangle. Find x and y. 0
12 Refer to the figure. ARM, MAX, and XFM are all isosceles triangles. 34. What is m MAX? 35. What is m ARM? 36. Which segment is the shortest possible distance from point D to plane P?
13 37. Determine the relationship (<,>,=) between CPV and CTK 38. Name the shortest and longest side of ABC. Determine whether the given measures can be the lengths of the sides of a triangle. Write yes or no. Explain , 6, 7
14 Refer to the figure to determine which is a true statement for the given information. 40. KN is an altitude. 4. KN is a median. 4. NK is an angle bisector. 3
15 43. AC is a perpendicular bisector and B = 49. Find the value of x, y, and the measure of CAB. Put your final answer on the appropriate line. x = y = m CAB = 4
16 44. Write a twocolumn proof for the problem. 6 steps Given: AB ED C is the midpoint of BD B and D are right angles Prove: ABC EDC A B C D E Statements Reasons 5
17 KEYSTONE RefEFERENCE GEOMETRY FORMULA SHEET PAGE Formulas that you may need to solve questions on this exam are found below. You may use calculator π or the number 3.4. Properties of Circles Right Triangle Formulas Angle measure is represented by x. Arc measure is represented by m and n. Lengths are given by a, b, c, and d. x n Inscribed Angle x = n a b c Pythagorean Theorem: If a right triangle has legs with measures a and b and hypotenuse with measure c, then... a + b = c x n m d a x c b n a x n b m c a m b n x c d TangentChord x = n Chords a b = c d x = (m + n) TangentSecant a = b (b + c) x = (m n) Secants b (a + b) = d (c + d ) x = (m n) opposite hypotenuse θ adjacent Trigonometric Ratios: opposite sin θ = hypotenuse adjacent cos θ = hypotenuse tan θ = Coordinate Geometry Properties opposite adjacent Distance Formula: d = (x x ) + (y y ) x Midpoint: + x, Slope: m = y y x x PointSlope Formula: (y y ) = m(x x ) Slope Intercept Formula: y + y y = mx + b Standard Equation of a Line: Ax + By = C a Tangents m n b x a = b x = (m n) Copyright 0 by the Pennsylvania Department of Education. The materials contained in this publication may be duplicated by Pennsylvania educators for local classroom use. This permission does not extend to the duplication of materials for commercial use.
18 KEYSTONE RefEFERENCE GEOMETRY FORMULA SHEET PAGE Formulas that you may need to solve questions on this exam are found below. You may use calculator π or the number 3.4. Plane Figure Formulas Solid Figure Formulas s s P = 4s A = s s l w h SA = lw + lh + wh V = lwh w l P = l + w A = lw r SA = 4ϖr 4 V = ϖr 3 3 a b h P = a + b A = bh h SA = ϖr + ϖrh V = ϖr h c a h b d P = a + b + c + d A = h(a + b) h r r SA = ϖr + ϖr r + h V = ϖr h 3 c b h d P = b + c + d A = bh h SA = (Area of the base) + (number of sides)(b)( ) r C = ϖr A = ϖr base b b V = (Area of the base)(h) 3 Sum of angle measures = 80(n ), where n = number of sides Euler s Formula for Polyhedra: V E + F = vertices minus edges plus faces = Copyright 0 by the Pennsylvania Department of Education. The materials contained in this publication may be duplicated by Pennsylvania educators for local classroom use. This permission does not extend to the duplication of materials for commercial use.
College Prep Geometry MIDTERM STUDY GUIDE. Mrs. Miller. Name: Due: Thursday, January 9, 2014
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