Geometry Honors Name: Chapter 5 Day 1 HW Date:
Transcript of Geometry Honors Name: Chapter 5 Day 1 HW Date:
Geometry Honors Name:_____________________ Chapter 5 Day 1 HW Date:______________________ 327-331; 10, 12, 14, 18, 22-26e 1. Find each measure.
a. PS
b. EG c. SW
2. Point D is the circumcenter of โณ ๐ด๐ต๐ถ. List the segment congruent to ๐ต๐น. 3. Find each measure
a. โ ๐ท๐ต๐ด
b. XA c. PN
28, 30, 38, 46 4. Point P is the incenter of โณ ๐ด๐ธ๐ถ. Find each measure.
a. DE
b. ๐โ ๐ท๐ธ๐ 5. Write a two-column proof. Given: โณ ๐ด๐ต๐ถ, angle bisectors ๐ด๐ท,๐ต๐ธ, and ๐ถ๐น ๐พ๐ โฅ ๐ด๐ต,๐พ๐ โฅ ๐ต๐ถ,๐พ๐ โฅ ๐ด๐ถ Prove: ๐พ๐ = ๐พ๐ = ๐พ๐
Statements Reasons
6. Find the coordinates of the circumcenter of the triangles with the given vertices. Explain.
๐ฝ 5,0 ,๐พ 5,โ8 , ๐ฟ(0,0)
48, 54, 55, 56 7. Brookeโs talking horses are arguing about who is correct. Marbury insists that from the information supplied in the diagram, one can conclude that K is on the perpendicular bisector of ๐ฟ๐. Chicken disagrees. Is either correct? Explain why. 8. Compare and contrast perpendicular bisectors and angle bisectors of a triangle. 9. An object is projected straight upward with an initial velocity v meters per second from an initial height of s meters. The height h in meters of the object after t seconds is given by โ = โ10๐ก! + ๐ฃ๐ก + ๐ . Sully is standing at the edge of a balcony 54 meters above the ground and throws a ball straight up with an initial velocity of 12 meters per second. After how many seconds will it hit the ground?
A 3 seconds B 4 seconds C 6 seconds D 9 seconds 10. Write an equation in slope-intercept form that describes the line containing the points โ1,0 and (2,4).
57, 58. 338-341; 8, 12 11. A line drawn through which of the following points would be a perpendicular bisector of โณ ๐ฝ๐พ๐ฟ? F T and K G L and Q H J and R J S and K 12. For ๐ฅ โ 3, !!!!
!!!= ?
A ๐ฅ + 9 B ๐ฅ + 3 C ๐ฅ D 3 13. In โณ ๐๐๐, ๐๐ฝ = 9,๐๐ฝ = 3,๐๐ = 18. Find the length of SV. 14. Find the coordinates of the centroid of the triangle with the given vertices.
๐ 5,7 ,๐ 9,โ3 ,๐(13,2)
14, 16, 18, 22, 24 15. Find the coordinates of the orthocenter of the triangle with the given vertices.
๐ โ4,8 , ๐ โ1,5 ,๐(5,5)
16. Identify each segment ๐ต๐ท as an altitude, median, or perpendicular bisector.
a.
b.
17. Complete the statement for โณ ๐ ๐๐ for medians ๐ ๐, ๐๐ฟ, and ๐๐พ, and centroid J
๐ฝ๐ = ๐ฅ(๐๐พ) 18. If ๐ธ๐ถ is an altitude of โณ ๐ด๐ธ๐ท, ๐โ 1 = 2๐ฅ + 7, and ๐โ 2 = 3๐ฅ + 13, find ๐โ 1 and ๐โ 2.
32, 37 19. Write an algebraic proof. Given: โณ ๐๐๐,with medians ๐๐ ,๐๐,๐๐ Prove: ๐โ 1+๐โ 2 = ๐โ 6+๐โ 7
Statements Reasons
20. The lunch lady says that based on the figure provided, !
!๐ด๐ = ๐ด๐ท. Dalton
explains to the lunch lady that that cannot be correct. What reason did Dalton use to correct the culinary connoisseur?
44-47 21. In the figure, ๐บ๐ป โ ๐ป๐ฝ. Which must be true? A ๐น๐ฝ is an altitude of โณ ๐น๐บ๐ป. B ๐น๐ฝ is an angle bisector of โณ ๐น๐บ๐ป. C ๐น๐ฝ is a median of โณ ๐น๐บ๐ป. D ๐น๐ฝ is a perpendicular bisector of โณ ๐น๐บ๐ป. 22. What is the x-intercept of the graph 4๐ฅ โ 6๐ฆ = 12? 23. Four students have volunteered to fold pamphlets for a local community action group. Which student is the fastest? F Deron G Neiva H Quinn J Sarah 24. 80 percent of 42 is what percent of 16?
A 240 B 210 C 150 D 50