Chapter 2 QUIZ. Section 2.1 The Parallel Postulate and Special Angles

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1 Chapter 2 QUIZ Section 2.1 The Parallel Postulate and Special Angles (1.) How many lines can be drawn through point P that are parallel to line? (2.) Lines and m are cut by transversal t. Which angle corresponds to 2. (3.) Lines and m are cut by transversal t. Along with 4, which angle forms a pair of alternate interior angles? (4.) If m and m 3= 71, find m 7. (5.) If m and m 3= 71, find m 5. Exercises 2 5 (6.) ABC is obtuse. If DB AB and EB BC, what type of angle is DBE? (7.) In a plane, lines r and s are both parallel to v. How are r and s related? (8.) AB CD and transversal EF. If m 2= x degrees, what expression in x represents m 3? (9.) AB CD and transversal EF. If m 1 = 108 and QR bisects FQD, what is m RQD? Exercises 8 10 (10.) AB CD and transversal EF. State the postulate, theorem or corollary that allows you to conclude that 5 4.

2 Section 2.2 Indirect Proof (1.) Classify the following implication as true or false: If two angles are congruent, these angles are right angles. (2.) State the converse of the statement given in number 1. (3.) State the contrapositive of the statement below: If an angle is a straight angle, then it measures 180. (4.) When an implication is true, which statement ( the converse, the inverse, or the contrapositive ) must also be true? (5.) State the conclusion of the following argument: (i) If a published novel reaches the best-seller list, it is a success. (ii) The published novel Natalie in Naples was not considered a success. (6.) State the conclusion of the following argument: (i) m 1 > 90 and m (ii) 1 is not a straight angle. (7.) Write the first statement of this indirect proof: Given: RS is not perpendicular to RT Prove: 1 is not a right angle. (8.) Write the first statement of this indirect proof: Given: AM MB Prove: M is the only midpoint of AB (9.) What statement is contradicted in an indirect proof leads to this situation: Rays SV and SW are both bisectors of RST? (10.) What statement is contradicted if an indirect proof leads to this situation: For BC, its length is BC = 0.

3 Section 2.3 Proving Lines Parallel (1.) In the drawing, m 3= 72. Determine m 7 so that lines and m are parallel. (2.) If angles 3 and 5 are supplementary, can you conclude that lines and m are parallel? (3.) If m 3= 2x and m 6= 3x 65, find x so that m. Exercises 1 3 (4.) If 5 7, which lines ( r and s or t and v or neither ) must be parallel? (5.) Suppose that r s and t v. If m 1 = 111, find m 16. (6.) If r s and s t, how are s and v related? Exercises 4 6 For exercises 7 10, fill in the missing reasons in the following proof. Given: ED bisects Prove: DE CB AEC and 3 1 Statements Reasons (1) ED bisects AEC (2) 1 2 (3) 3 1 (4) 2 3 (5) DE CB (7) (8) (3) Given (9) (10)

4 Section 2.4 The Angles of a Triangle (1.) In ABC, AB = 4, AC = 4, and BC = 6. What type of triangle is ABC? (2.) In DEF, m E = 90. What type of triangle is DEF? (3.) In GHK, m G = 61 and H = 46. Find m K. (4.) If m M = 25 and m N = 35 in MNP, what type of triangle is MNP? (5.) If m ABD = 74 and m A= m C, what is the measure of A? (6.) If m ABD = 74 and m A = 43, what is the measure of C? Exercises 5 & 6 (7.) In a triangle, the measures of the angles are m 1= x + 5, m 2= x + 6, and m 3= 2x 43. Find the value of x. (8.) In the drawing, 3 6. How are angles 2 and 5 related? (9.) In the drawing, m 7 = 116. Determine the sum m 2+ m 3. Exercises 8 & 9 (10.) Classify as true or false. The sum of the three exterior angles of any triangle ( one at each vertex ) is always 360.

5 Section 2.5 Convex Polygons (1.) What name is given to a polygon that has exactly six sides? nn ( 3) (2.) Using D =, what is the total number of diagonals in a 2 polygon with 8 sides? (3.) What is the sum of the interior angles of a polygon that has 5 sides? (4.) What word is used to characterize a polygon that has all its angles congruent? (5.) What is the measure of each interior angle of a regular pentagon (5 sides?) (6.) What is the measure of each exterior angle of an equiangular quadrilateral ( also known as a rectangle )? (7.) Because it has 5 points, what name is given to the star shaped figure at the right? (8.) If the sum of all interior angles of a polygon is 1440, how many sides does a polygon have? (9.) To construct a STOP sign in the shape of a regular octagon, a cut needs to be made at point A. How large is JAB? (10.) In any polygon, each interior angle has an adjacent exterior angle. How is every such pair of angles related?

6 Section 2.6 Symmetry and Transformation (1.) Which letter has both point symmetry as well as line symmetry? A N H (2.) Which type of triangle must have line symmetry? scalene triangle isosceles triangle obtuse triangle (3.) Which type of regular polygon has point symmetry? equilateral triangle square regular pentagon (4.) For a rectangle, how many different lines of symmetry are there? (5.) Can a geometric figure have more than one point of symmetry? (6.) A slide of ABC produces its image DEF. How are ABC and DEF related? (7.) Following a translation (or slide), the image of quadrilateral RSTV is quadrilateral WXYZ. Which line segment is the pre-image of side YZ? (8.) Let point C be a point to the left of the vertical line AB. For ABC, the reflection across AB is ABD. While D is the image of point C, which point is the image of B? (9.) Square ABCD is rotated 90 about its point of symmetry, point P. For the rotation, the image of vertex A is vertex B. What is the image of point D? (10.) The Chrysler logo has a point of symmetry. What is the measure of the smallest angle of rotation for which the image coincides with the given logo?