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
Euler angles wikipedia , lookup
Golden ratio wikipedia , lookup
History of trigonometry wikipedia , lookup
Trigonometric functions wikipedia , lookup
Rational trigonometry wikipedia , lookup
Reuleaux triangle wikipedia , lookup
Euclidean geometry wikipedia , lookup
Pythagorean theorem wikipedia , lookup
Geometry Name___________________ Chapter 3 Review Date__________ Period____ For questions 1 – 5, write A for always, S for sometimes, or N for never. 1. A right triangle has three right angles. ______ 2. An isosceles triangle is a right triangle. ______ 3. The base of an acute isosceles triangle is shorter than either leg. ______ 4. The altitude of a triangle bisects the side to which it is drawn. ______ 5. A median of a triangle bisects the angle it is drawn from. ______ 6. List the three ways to classify a triangle by side length. 7. Write the definition of an altitude and a median. 8. What information is needed to prove these two triangles congruent using HL postulate. 9. Name the base angles if LB BE 10. In the diagram, if UM AS then what property justifies UA MS . Solve problems 11 and 12 by referring to the diagram and the information given W Given: ASU WIN 15 4x + 6 S 11. Find the measure of W . ______ 10 A 28 91 12. Solve for x: I 61 U 13. Given: 5 6 HN is the altitude to AD Prove: Triangle HAD is isosceles. Statement Reason 1. 2. 3. 4. 5. 6. 7. 8. 9. 14. Given: NE SE EO is an altitude. Prove: EO bisects NES 1. 2. 3. 4. 5. 6. 7. 8. 9. Statement Reason 6 N In problems 15-18 “mark” the diagram with the given information and then state the reason for the congruence (SSS, SAS, ASA, or HL). 3 15. 1 2 ______ B 16. ______ 4 A 1 2 and 3 4 C D BD is an altitude of ABC AD DC 17. ______ A E 18. A ______ B B C D C ED BC A D E C is the midpoint of AE and DB 19. Reflect the following triangle over the y-axis; write the coordinates of the new triangle. In problems 20-25 name the triangles that are congruent and give the appropriate congruence theorem (SSS, SAS, ASA, or HL). 20. ABC __________ ABC __________ 21. _________________ _________________ 22. ABC __________ ABC __________ 23. _________________ _________________ 24. ABC __________ ABC __________ 25. _________________ _________________ 26. The perimeter of NAU is 55. NA = x + 4, AU = 24, and NU = 5x + 3. By solving for x, determine whether NAU is scalene, isosceles, or equilateral. A 24 x+4 N U 5x + 3 27. In triangle with vertices A, B, and C, angles B and C are congruent. AB = 6x +7, AC = 5x + 11 and BC is 3x + 2y. How long is BC in terms of “y”?