* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Name:
Projective plane wikipedia , lookup
Perspective (graphical) wikipedia , lookup
Algebraic geometry wikipedia , lookup
Cartesian coordinate system wikipedia , lookup
History of trigonometry wikipedia , lookup
Integer triangle wikipedia , lookup
Lie sphere geometry wikipedia , lookup
Pythagorean theorem wikipedia , lookup
Geometrization conjecture wikipedia , lookup
Analytic geometry wikipedia , lookup
Perceived visual angle wikipedia , lookup
Duality (projective geometry) wikipedia , lookup
Trigonometric functions wikipedia , lookup
Multilateration wikipedia , lookup
Euler angles wikipedia , lookup
Compass-and-straightedge construction wikipedia , lookup
History of geometry wikipedia , lookup
Rational trigonometry wikipedia , lookup
Geometry Name: _________________________ Date: _______________ Per.: ______ MIDTERM EXAM: Chapter 1 Review Key Concepts & Skills Use defined and undefined terms (e.g., points, lines, planes, rays, segments, collinear, coplanar, betweenness, congruent, etc.) Identify or sketch skew and parallel lines Sketch, label, name basic elements of Geometry Sketch intersections of lines and planes Apply segment postulates (e.g., Segment Addition Postulate, Ruler Postulate) and the distance formula to find measures of segments. Classify angles (acute, obtuse, etc.) and apply angle postulates (e.g., Angle Addition Postulate) to find angle measures. Name angles and find measures using a protractor Bisect segments and angles. Find the midpoint of a segment on the coordinate plane. Apply the properties of a bisector to solve problems. Identify vertical angles, linear pairs, complementary angles, and supplementary angles. Solve problems by applying geometric properties and algebra skills (e.g., find angle measures given algebraic expressions for angle values). Find the perimeter, circumference, and area of squares, rectangles, triangles, and circles (common plane figures) Formulas Distance between 2 points: MD/1-08/Ch. 1 MT Review d (x2 x1)2 (y2 y1)2 Midpoint x2 x1 y2 y1 , 2 2 1 Geometry Problems I. Segments, distance, midpoint 1) Use the distance formula to determine if PQ QR given P (-4, 3), Q (-2, 1), R (0, -1) 2) Using points P, Q, & R from #1, find the midpoints of PQ, QR, & PR . 3) Q is between P and S. R is between Q and S. S is between Q and T. PT = 30, QS = 16, and PQ = QR = RS. Find PQ, ST, and RP. 4) Find the length of segments AB, BC, and CD given: AD = 30, AB = 2x + 2, BC = 4x – 1, and CD = 3x – 7. MD/1-08/Ch. 1 MT Review 2 Geometry II. Angles 1) Classify the angle as acute, right, obtuse, or straight. a) mKLM = 180 b) mA = 150 c) mY = 45 2) Find the measure of the unknown angle. a) mDEF b) mHJL c) mQNM 3) Ray QS is the bisector of PQR. Find any angle measures not given in the diagram. a) b) c) 4) Use the diagram to the right to decide whether the statement is always, sometimes, or never true. a) If m2 = 115, then m3 = 65. b) If m1 = 40, then m3 = 50. c) 3 and 4 are congruent. d) 1 and 4 are complements. MD/1-08/Ch. 1 MT Review 3 Geometry 5) A and B are complementary. Find mA and mB. a) mA = 7x + 1, mB = 5x – 7 b) mA = 5x + 11, mB = 2x – 5 6) Ray BD bisects ABC. Find the value of x. a) b) 7) Find the values of the variables. a) MD/1-08/Ch. 1 MT Review b) 4 Geometry III. Perimeter, Circumference, and Area. Find the perimeter (or circumference) and area of the figure described. 1) Rectangle with length 10 cm and width 4.5 cm. 2) Circle with radius 9 in. (Use = 3.14) 3) Triangle defined by A (-6, 0), B (2, 0), and C (-2, -3) 4) A square garden has sides of length 14 ft. IV. Points, Lines, Planes. Decide whether the statement is true or false. 1) Point C lies on line l. 2) Point E lies on AB . 3) Points D, A, and B are collinear. 4) Points D, A, and B are coplanar. 5) Point C lies on line 6) Lines l and m. m intersect at E. MD/1-08/Ch. 1 MT Review 5