Study Guide and Review

Transcription

1 Fill in the blank in each sentence with the vocabulary term that best completes the sentence 1 A is a flat surface made up of points that extends infinitely in all directions A plane is a flat surface made up of points that extends infinitely in all directions Therefore, the correct answer is plane 2 A set of points that all lie on the same line are said to be A set of points that all lie on the same line are said to be collinear points Therefore, the correct answer is collinear 3 If two lines intersect to form four right angles, the lines are called If two lines intersect to form four right angles, the lines are called perpendicular 7 Name a point that is not contained in any of the three lines a, b, or c Here, W is a point on the plane R and is not on any of the lines on the plane 8 Give another name for plane WPX 9 The plane WPX is also named as plane R Name the geometric term that is best modeled by each item In the figure, two flat surfaces intersect each other The two flat surfaces model two planes Since the intersection of two planes form a line, the item models a line 4 If the sum of the measures of two angles is 180, then the angles are called angles If the sum of the measures of two angles is 180, then the angles are called supplementary angles Use the figure to complete each of the following 10 Each bead denotes a location So, it models a point 5 Name the intersection of lines a and c The lines a and c intersect at the point P 6 Give another name for line b There are two point S and T marked on the line b So, the line b can also be called esolutions Manual - Powered by Cognero Page 1

2 Find the value of the variable and XP, if X is between P and Q 11 XQ = 13, XP = 5x 3, PQ = 40 Here X is between P and Q So, PQ = XP + XQ 14 P(2, 1) and Q(10, 7) We have XQ = 13, XP = 5x 3, and PQ = = x 3 30 = 5x 6 = x The distance between P and Q is or M(9, 2) and N( 1, 4) So, XP = 5(6) 3 = XQ = 3k, XP = 7k 2, PQ = 6k + 16 Here X is between P and Q So, PQ = XP + XQ We have XQ = 3k, XP = 7k 2, PQ = 6k k + 16 = 7k 2 + 3k 6k 10k = k = 18 k = 45 The distance between points M and N is 16 J(3, 2) and K(6, 5) So, XP = 7(45) 2 = 295 Find the distance between each pair of points 13 A( 3, 1) and B(7, 13) The distance between J and K is The distance between points A and B is esolutions Manual - Powered by Cognero Page 2

3 Find the coordinates of the midpoint of a segment with the given endpoints 18 L( 3, 16), M(17, 4) Use the Midpoint Formula Substitute Find the coordinates of the missing endpoint if M is the midpoint of 20 X( 11, 6), M(15, 4) Let the coordinates of Y be (x, y) Then by the Midpoint Formula, Write two equations to find the coordinates of Y The midpoint of is (7, 10) 19 C(32, 1), D(0, 12) Use the Midpoint Formula Substitute The midpoint of is (16, 65) The coordinates of Y are (41, 14) 21 M( 4, 8), Y(19, 0) Let the coordinates of X be (x, y) Then by the Midpoint Formula, Write two equations to find the coordinates of X The coordinates of X are ( 27, 16) esolutions Manual - Powered by Cognero Page 3

4 For Exercises 25 28, refer to the figure below 32 If m SXW = 5x 16, find the value of x so that Since 25 Name the vertex of 7 Here, 7 is same as the angle CGJ So, the vertex of the angle is G 26 Write another name for 4 Here, 4 is same as the CDG 27 Name the sides of 2 Here, 2 is same as the ACH Therefore, its sides are For Exercises 30 32, refer to the figure below 34 That is, 5x 16 = 90 Add 16 to both sides 5x = 106 Divide both sides by 5 x = 212 Name each polygon by its number of sides Then classify it as convex or concave and regular or irregular The polygon has 3 sides So, it is a triangle No line containing any of the sides will pass through the interior of the triangle, so it is convex All of the sides are congruent, so it is equilateral All of the angles are congruent, so it is equiangular Since the polygon is convex, equilateral, and equiangular, it is regular So this is a regular triangle 30 Name an angle supplementary to TVY Supplementary angles are two angles with measures that have a sum of 180 Here, TVR is supplementary to TVY 31 Name a pair of vertical angles with vertex W Vertical angles are two nonadjacent angles formed by two intersecting lines Here, QWP and XWV are a pair of vertically opposite angles esolutions Manual - Powered by Cognero Page 4

5 35 The polygon has 12 sides So, it is a dodecahedron Four of the lines containing the sides of the polygon will pass through the interior of the dodecahedron, so it is concave Only convex polygons can be regular, so this is an irregular dodecahedron esolutions Manual - Powered by Cognero Page 5