19. Study this page and/or watch the video on the multimedia text to copy the angle below.
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1 Chapter 12 Study Guide Section What are the symbols for similarity and congruence? 2. What is meant by saying figures are similar, and saying figures are congruent? What is a rep-tile? 4. What is meant by congruent segments and congruent angles? 5. Are all circles similar? 6. About circles: know center, radius, 7. What two instruments can be used in Euclidean constructions? 8. What are the rules of Euclidean constructions? Know how to construct a circle with a given radius and given center point. Radius (Make your own point on another sheet of paper) You may go online to the multimedia text and click on the camera icon on this page Know how to copy a segment using only a compass. See the multimedia text. 11. What is the definition of congruent triangles? 12. What does cpctc mean? Do the Now Try This 12:2 14. Do example Does one have to know that all sides are congruent and all angles are congruent (all 6 parts) to know that two triangles are congruent? 16. What does SSS mean? Do example In each congruence, make sure that the vertices of each triangle are listed in the order that their congruence occurs Construct a triangle congruent to the one below. Use another piece of paper. Look at the multimedia text and click on the camera icon on this page if you need to see better instructions via video. 19. Study this page and/or watch the video on the multimedia text to copy the angle below.
2 Construct a triangle given two sides and the included angle. The two sides are to be the following lengths. and The angle is to be the size of the one in #19 above. Use another sheet of paper What does SAS mean? 22. Do example Does SSA imply that two triangles are congruent. Give example In SSA, if the angle is specifically a right angle, will there be congruence? 25. What does HL mean? 26. What is an angle bisector? 27. What is a perpendicular bisector? 28. If a point is equidistant from the endpoints of a segment, will it be on the perpendicular bisector of that segment? What can be said about the base angles in an isosceles triangle? 30. Will the angle bisector of the vertex angle of an isosceles triangle also be a perpendicular bisector of the base of that isosceles triangle? 31. What is the altitude of a triangle? 32. Will the altitude to the base of an isosceles triangle also be a perpendicular bisector? 33. Draw a triangle in which the altitude does not intersect the opposite side of the triangle. 34. How is the distance between a point and a line determined? Construct the perpendicular bisector to the segment below: 36. What does it mean for a triangle to be circumscribed? 37. Circumscribe a circle about the triangle below:
3 Do the Now Try This 12-3 on another sheet of paper According to the theorem on this page what must be true of a quadrilateral which may be circumscribed? 40. When can a kite be circumscribed? Reasonable problems to work: Pg. 719 #1,2,3,6,8,12,13, 14 pg. 720 # 5,6, pg. 721 #12,16, 5,7 Pg 722 #13,15,16,17,18,21
4 Chapter 12, Section What does ASA mean? Do example What does AAS mean? Do example What does Theorem 12-8 say about parallelograms? 6. The diagonals of a parallelogram each other Do Now Try This Know all the facts on this page What is a median? If all the sides of a quadrilateral are congruent to all the sides of another quadrilateral, will they be congruent? Reasonable problems to work: P. 729 #3,5,6,7,8, pg. 730 #9,10,11,13,14,17,18,19,20, 3,4 Pg. 731 # 5,7,9,19,20, p. 732 #4, 5,7, Pg. 733 #18 Section What is a rhombus? What are three facts about the diagonals of a rhombus? 3. Be able to construct a line through a point P that is parallel to a given line. Do the construction below.. P Be able to construct the angle bisector of an angle. Bisect the angle below:
5 What is a Mira? 6. Construct a line perpendicular to a line through a point P not on the line..p Know how to construct the bisector of a line segment. 8. Know how to construct a segment perpendicular to a line from a point on that line.. P Study example on this page. Be able to construct the altitude in any triangle What is an important property of an angle bisector? How can one construct the incircle of a triangle? 12. What is meant by the tangent to a circle?
6 13. What is an incenter? What does inscribed mean? 14. How can a circle be inscribed in a square? Reasonable problems to work: Pg. 741 #2,5,8, pg. 742 # 13, 14, 15, 17 pg. 743 #14, Section 4 1. What is meant by similar figures? 2. What is meant by scale factor? 3. What are similar triangles (formal definition)? 4. What is the formal definition for similar polygons? 5. What is the SSS similarity theorem? 6. What is the SAS similarity theorem? 7. Read and work this entire schoolbook page. 8. What is the AA similarity theorem for triangles? 9. Work examples and Do the Now Try This Do example IF you have trouble click on the icon by this example on the multimedia text. The camera icon shows how this is worked. The triangular icon gives a similar example to work. 12. Study the properties of proportion as they related to parallel lines. 13. Use the theorem to solve for x in the problem below x Study Thm & Be able to use construction methods to equally divide a segment into any given number of segments. 16. What is a midsegment? What is the midsegment theorem? 17. If a line bisects one side of a triangle and is parallel to another side then 18. Do example What is a median? 20. What is a center of gravity or centroid? 21. When the medians of a triangle intersect, they intersect at the centroid, but how does the centroid proportion the segments of the median? See example at the top of page. 22. How have similar triangles been used to make indirect measurements?
7 Work example Use the multimedia text with camera icon to furnish a video on how this is done. 24. What is slope? 25. Study the slopes on this page. What is the m in the equation y=mx + b? 26. Do example Reasonable problems to work: p. 756 #1-5 pg. 757 #8-12, 15, p. 759 # 11, 14,16, 4
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