Geometry SOL Review Packet QUARTER 3
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1 Geometry SOL Review Packet QUARTER 3
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3 Arc Length LT 10 Circle Properties Important Concepts to Know Sector Area It is a fraction of. It is a fraction of. Formula: Formula: Central Angle Inscribed Angle Relation to Measure of Intercepted Arc: Relation to Measure of Intercepted Arc: Interior Angle Exterior Angle Relation to Measure of Intercepted Arc: Relation to Measure of Intercepted Arc: Segments Intersecting Inside Circle Segments Intersecting Outside Circle Formula: Formula: Examples of SOL- Like Questions 1. What is m DAR in circle A? A. 17 B. 34 C. 56 D Two chords intersect with the measures shown in the drawing. What is the value of x? A. 8.0 B. 9.5 C D. 14.5
4 3. In the circle, what is the meausre of ABC? A. 30 B. 60 C. 120 D In circle O shown in the diagram below, chords AB and CD are parallel. If mab=104 and mcd=168, what is mbd? A) 38 B) 44 C) 88 D) In the diagram below of circle O, PAC and PBD are secants. If mcd = 70 and mab = 20, what is the degree measure of P? A) 25 B) 35 C) 45 D) Given: Circle T with WP = 36 centimeters. Which best represents the area of the shaded sector? A) 117π cm 2 B) 180π cm 2 C) 234π cm 2 D) 468π cm 2 7. Find the area of shaded sector of circle Q. Find the length of arc AB.
5 LT 11 Equations of Circles Important Concepts to Know Distance Formula (Pythagorean Theorem) Midpoint Formula [Finding Center] Equation of a Circle When writing, remember to on the center. If given a center and point on circle, If given endpoints of the diameter, 1. The endpoints of AB are A(- 4, 5) and B(2, - 5), what is the length of AB? Examples of SOL- Like Questions 2. What are the center and the radius of the circle whose equation is (x 3) 2 + (y + 3) 2 = 36? A. B. C. D. 2 A. center = ( 3,3); radius = 6 B. center = (3, 3); radius = 6 C. center = ( 3,3); radius = 36 D. center = (3, 3); radius = 36
6 3. Which equation represents the circle whose center is ( 2, 3) and whose radius is 5? 4. Write the equation of the circle shown here: A. (x + 2) 2 + (y 3) 2 = 25 B. (x 2) 2 + (y + 3) 2 = 25 C. (x + 2) 2 + (y 3) 2 = 5 D. (x 2) 2 + (y + 3) 2 = 5 5. A circle is represented by the equation x 2 + (y + 3) 2 = 13. What are the coordinates of the center of the circle and the length of the radius? A. B. C. D. 6. What quadrant is the equation below located in? A. I B. II C. III D. IV Find the midpoint of the segment joining the points (4, - 2) and (- 8,6). A. (6, 4) B. (- 6,- 4) C. (2, 2) D. (- 2, 2) 9. What is the equation of the circle with diameter endpoints (- 2, 4) and (6, 10)? 10. What is the equation of the circle with diameter endpoints (1, - 3) and (- 5, - 9)?
7 Polygon LT 12 Angles in Polygons Important Concepts to Know Finding the Number of Sides in a Polygon Regular Polygon Interior Angle Sum Theorem Exterior Angle Sum Theorem Finding ONE Interior Angle Finding ONE Exterior Angle 1. The Pentagon in Washington, D.C. is a regular pentagon as shown. What are the values of x and y in degrees? Examples of SOL- Like Questions 2. LeeAnn cut a piece of stained glass that is shaped like the hexagon below. What is the value of x? A) x = 128; y = 51.4 B) x = 120; y = 60 C) x = 108; y = 72 D) x = 72; y = 108 A) 114 B) 134 C) 314 D) 494
8 3. This figure is composed of an isosceles trapezoid and a regular octagon. What is the value of x? A) 100 B) 125 C) 135 D) A regular pentagon and a regular hexagon share a side as shown. What is the measure of exterior angle ABG? 5. If a regular polygon has an interior angle measure of 174 o, how many sides does the polygon have? 6. If a regular polygon has an exterior angle with a measure of 4 o, how many sides does the polygon have? 7. ABCDE is a regular pentagon. What is the measure of angle AEB? 8. The pentagon in the diagram below is formed by five rays. What is the degree measure of angle x?
9 LT 15 Quadrilateral Properties Important Concepts to Know Quadrilateral Venn Diagram Medians in a Trapezoid Quadrilaterals with Two Sets of Congruent Sides Quadrilaterals with Two Sets of Parallel Sides Quadrilaterals with 4 Congruent Sides Quadrilaterals with only Right Angles Quadrilaterals with Congruent Diagonals Quadrilaterals with Bisected Diagonals Examples of SOL- Like Questions 1. Which figure has all sides of equal measure but not necessarily all angles of equal measure? A. Square B. Rectangle C. Rhombus D. Trapezoid 2. In rectangle ABCD, the slope of AB is!. What is the! A. - 2 B.!! C.!! D. 2 slope of CD?
10 3. DEFG is a rhombus with m EFG = 28. What is m GDE? A. 14 B. 28 C. 30 D A rectangular rug is 24 feet long and 10 feet wide. A rhombus design is formed inside the rug by joining the midpoints of each side of the rectangle. What is the length of each side of the rhombus? A. 13 ft B. 26 ft C. 169 ft D. 240 ft 5. As shown in the diagram of rectangle ABCD below, diagonals AC and BD intersect at E. If AE = x + 2 and BD = 4x 16, then the length of AC is A) 6 B) 10 C) 12 D) In the diagram of trapezoid ABCD below AB DC, AD BC, m A = 4x + 20, and m C = 3x 15. What is m D? A) 25 B) 35 C) 60 D) Square ABCD has vertices A (- 2, - 3), B (4, - 1), C (2, 5) and D (- 4, 3). What is the length of a side of the square? 8. Find the length of AB if QRSP is a trapezoid. A) 2 5 B) 2 10 C) 4 5 D) 10 2
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