* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Week_13
Survey
Document related concepts
Technical drawing wikipedia , lookup
Rotation formalisms in three dimensions wikipedia , lookup
Riemannian connection on a surface wikipedia , lookup
Cardinal direction wikipedia , lookup
Pythagorean theorem wikipedia , lookup
Perspective (graphical) wikipedia , lookup
Integer triangle wikipedia , lookup
Line (geometry) wikipedia , lookup
History of the compass wikipedia , lookup
Multilateration wikipedia , lookup
History of trigonometry wikipedia , lookup
Rational trigonometry wikipedia , lookup
Trigonometric functions wikipedia , lookup
Euclidean geometry wikipedia , lookup
Transcript
WEEK 13 (assignments 42-45) Videos: Constructing Parallel Lines: http://www1.teachertube.com/viewVideo.php?video_id=203474&title=Parallel_Lines_Construction http://teachertube.com/viewVideo.php?video_id=120198&title=Constructing_Parallel_Lines Given a line and a point, construct a line through the point, parallel to the given line using Corresponding Angles (CA) 1. Begin with point P and 2. Draw an arbitrary line 3. Center the compass at 4. Set the compass radius to line k. through point P, intersecting point Q and draw* an arc the distance between the two line k. Call the intersection intersecting both lines. intersection points of the first point Q. Now the task is to Without changing the radius arc. Now center the compass construct an angle with of the compass, center it at at the point where the second vertex P, congruent to the point P and draw another arc intersects line PQ. Mark angle of intersection. arc. the arc intersection point R. 5. Label the new line PR 6. Box a statement to show (or cursive l) and the two 4 angles (example: 2 and 4). l the two angles are congruent, corresponding 2 2 4, CA, l ǁ k angles (CA), so line l is parallel to line k. *Note: these pair of angles can go in any of the four directions (in pairs) from the two vertices Q and P 11/29 homework (#42) Construct eight parallel line pairs, given a line and a point off the line. Make two each by constructing congruent angles for each pair of corresponding angles (CA's) from each of the four directions from the vertex (upper right, lower right, lower left, upper left). Make congruence statements for each. EC: construct a set of three parallel lines using CA's. 11/30 homework (#43) See steps on last pages Construct four parallel line pairs, given a line and a point off the line. Make four by constructing congruent angles for each pair of Alternate Exterior Angles (AEA's) - doing both the obtuse and acute angles (two times each). Make congruence statements for each construction. 12/2 homework (#44) Construct eight parallel line pairs, given a line and a point off the line. Make four by constructing congruent angles for each pair of Alternate Interior Angles (AIA's) - doing both the obtuse and acute angles (two times each). Make two by constructing supplementary angles for each pair of Same Side Interior Angles (SSIA's). Make two more by constructing a perpendicular transversal thru the point and then a new line perpendicular to the transversal at the point. Make construction statements for each. 12/3 homework (#45) Find the measures for all the interior angles (three triangles, and one quadrilateral) given a large triangle ABC, where AB=CB and two rays AF and CE that bisect angles A and C and intersect at point D in the center of the triangle and measure of angle CAB = 52 degrees. (see attachment for a figure of this exercise) WEEK 13 (assignment 45) Find the measures of each angle: Given: AB CB and AF bisects A and CE bisects C, and AF and CE intersect at point D, and mCAB = 52º B Angle 1 1 2 3 4 2 E 3 5 5 F 6 8 4 D 6 7 7 8 9 9 10 10 11 A 13 11 12 C 12 13 Measure Given a line and a point, construct a line through the point, parallel to the given line using Alternate Exterior Angles 1. Begin with point P and 2. Draw an transversal line 3. Center the compass at 4. Span the compass radius line k. through point P, intersecting point Q and draw* an arc to the distance between the line k. Label the intersection intersecting both lines. two intersection points of the point Q. Now construct an Without changing the radius first arc. Now center the angle with vertex P, of the compass, center it at compass at the point where congruent to one of the two point P and draw another the second arc intersects exterior angles (1 or 2) arc 180⁰ in the opposite transversal line PQ. Mark the at Q. direction (make sure they arc intersection point R. both pass thru the transversal). R P • P • Q Q • 1 5. Label the new line PR k 2 R P (or cursive l) and the two l Q • 1 2 Q • 1 2 k • 1 2 6. Box a statement to show the two angles are 4 P • angles (example: 2 and 4). P • congruent, corresponding 2 4, AEA, l ǁ k angles (CA), so line l is k parallel to line k. *Note: these pair of angles can be either the obtuse or acute angles (in pairs) from the two vertices Q and P k