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STAIR: Project Development Geometry Review & Exercises Presented by Joys Simons Lines Introduction Circles Introduction Lines Questions Circles Questions Answers to Lines Answers to Circles Reminder - Lines Reminder - Circles Angles Introduction Lines Quiz Angles Questions Angles Quiz Answers to Angles Circles Quiz Reminder - Angles Lines Q. Review Angles Q. Review Circles Q. Review In geometry, a basic building block is the line, which is understood to be a “straight” line. It is also understood that lines are infinite in length. In the figure below, A and B are points on line . • What is it called? (That part of line from A to B, including the endpoints A and B ) • Which is ? in length? . That part of line from A to B, including the endpoints A and B, is called a line segment, which is finite in length. . Sometimes the notation “AB” denotes line segment AB and sometimes it denotes the length of line segment AB. The exact meaning of the notation can be determined from the context. . Lines 1 and 2 , shown below, intersect at point P. Whenever two lines intersect at a single point, they form four angles. . • What do the opposite angles called? • What is the sum of the measures of the four angles? . Opposite angles, called vertical angles, are the same size, i.e., have equal measure. Thus, APC and DPB have equal measure, and APD and CPB also have equal measure. The sum of the measures of the four angles is 360°. An angle that measures 90 is called a right angle, and an angle that measures 180 is called a straight angle. The set of all points in a plane that are a given distance r from a fixed point O is called a circle. The point O is called the center of the circle, and the distance r is called the radius of the circle. Also, any line segment connecting point O to a point on the circle is called a radius. . • What is it called for any line segment that has • . its endpoints on a circle, such as PQ below? What is it called for any chord that passes through the center of a circle? Any line segment that has its endpoints on a circle, such as PQ below, is called a chord. Any chord that passes through the center of a circle is called a diameter. . the diameter of a circle is always equal to twice its radius. The distance around a circle is called its circumference. In any circle, the ratio of the circumference c to the diameter d is a fixed constant, denoted by the Greek letter Л. . Lines l and m below are parallel. Find the values of x and y. A x=57, y=138 B X=50, y=140 C x=55, y=145 In the figure below, AC = BC. Find the values of x and y. A x=65, y=120 B X=70. y=125 C x=75, y=130 The figure below shows two concentric circles each with center O. If the larger circle has radius 12 and the smaller circle has radius 8, find the area of the shaded region. A The area = 78 Л B The area = 75 Л C The area = 80 Л Back to Lines Quiz Back to Angles Quiz Back to Circles Quiz Back to Lines Quiz Back to Angles Quiz Back to Circles Quiz Geometry review & Exercises Geometry Review Lines Angles Circles Geometry Exercises Lines Angles Circles Quiz & Interaction will be placed here Lines l and m below are parallel. Find the values of x and y. From our Lines introduction chapter, we knew when two lines are parallel, the angles on the same side will be equal; we should also remember, the opposite angles are equal; since the opposite angle of 57° has already provided to us, that’s why the x = 57. On the other hand, we knew that the straight angle = 180° and the opposite angle is 42° (It is the provided information.) So y = 180 - 42 = 138. Please contact me at [email protected] if you need help. In the figure below, AC = BC. Find the values of x and y. From our Angles introduction chapter, we knew that if a triangle has two sides of equal length, then the measures of the angles opposite the two sides are equal. The information of AC = BC was provided, and we knew the information of 125°, so 180° – 125° = 55° (That means both Angles BAC and ABC = 55°.) Thus, X = 180 – 55 – 55 = 70; Y = 180 – 55 = 125. Please contact me at [email protected] if you need help. The figure below shows two concentric circles each with center O. If the larger circle has radius 12 and the smaller circle has radius 8, find the area of the shaded region. From our Circles introduction chapter, we knew the area = radius² Л. Thus, the area of the larger circle = 12² Л = 144 Л ; and the area of the smaller circle = 8² Л = 64 Л; so the area of the shaded region should be: 144 Л - 64 Л = 80 Л. Please contact me at [email protected] if you need help.