Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Honors Geometry Unit #2 Review Topics: Points, lines, planes, collinear, coplanar, notation, midpoint formula Union and intersection Angles, notation, classification, Congruence Midpoints, bisectors, and trisectors Counterexamples Assumptions about diagrams Perpendicular, complementary, supplementary Vertical angles and the Vertical Angle Theorem (VAT) Algebra review of solving quadratic equations by factoring and solving systems of linear equations Review Problems: 1. Refer to the figure to the right. a. Name three collinear points. b. Name four coplanar points. c. Name three noncollinear points. d. Name four noncoplanar points. e. Find R DF . f. Find HI JI . g. Find CG FG h. Find P R. i. Find IL LI . H E A P F I L D A J R G K B C 2. Graph A(-8,3), B(5,1), C(3,-6), and D(-2,-3). a. Draw CA . b. Find AD. c. Find the midpoint of BC . d. Find the slope of AD and the slope of BC . Are the segments parallel, perpendicular, or neither? e. Find and label a point F so that CF BC . f. Find and label a point G so that AGD is a straight angle. 3. If E is acute and mE = 6x + 15, find all possible values of x. 4. If PQR is a straight angle and mPQR = 3 x 2 6 x 108 , find all possible values of x. 5. In the diagram below, JK ML . Is M a right angle? Give an explanation for your answer. 6x - 2 J M 12x° 5x + 5 K L 6. Draw a diagram to illustrate the problem, then give an answer: ABC is trisected by BD and BE . DBE is bisected by BX . If mABC = 81°, what is mDBX? 7. Two complementary angles are in a ratio of 7:8. Find the measure of the smaller angle. 8. One of two supplementary angles is 30 more than 5 times the other. What is the measure of the larger angle? 9. If M is the midpoint of AB , AM 2 x 58 , find BM. x 1 and AB 3 5 10. Find the measure of each numbered angle in the diagram below. 6 4 3 1 2 33° 5 11. In the diagram below, m1 5 x 2 y, m 2 6 x 10 y 7 , and m3 80 7 y . Are the lines perpendicular? Show all of your work and give an explanation of your answer. 2 1 3 ***Note: In addition to problems similar to the ones above there will be some True/False questions on your test. Unit #2 Review Key: 1. a. ex: H,I,J b. ex: A,E,F,D c. ex: H,I,L d. ex: H,I,L,E e. D f. HJ g. G h. AD i. IL 5 2. b. 6 2 c. (4, ) d. 1 and 2/7; neither 2 3. -5/2 < x < 25/2 4. -6 and 4 5. Since x is 7, mM = 84°, so M is not a right angle. 6. 13.5° 7. 84° 8. 155° 9. 7 10. m1 = m2 = 90°; m3 = 147°; m4 = 33°; m5 = m6 = 147° 11. x = 15 and y = -1; m1 = 73° so the lines are not perpendicular.