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 β³ π΄π΅πΆ. List the segment congruent to π΅πΉ. 3. Find each measure
a. β π·π΅π΄
b. XA c. PN
28, 30, 38, 46 4. Point P is the incenter of β³ π΄πΈπΆ. Find each measure.
a. DE
b. πβ π·πΈπ 5. Write a two-column proof. Given: β³ π΄π΅πΆ, angle bisectors π΄π·,π΅πΈ, and πΆπΉ πΎπ β₯ π΄π΅,πΎπ β₯ π΅πΆ,πΎπ β₯ π΄πΆ Prove: πΎπ = πΎπ = πΎπ
Statements Reasons
6. Find the coordinates of the circumcenter of the triangles with the given vertices. Explain.
π½ 5,0 ,πΎ 5,β8 , πΏ(0,0)
48, 54, 55, 56 7. Brookeβs 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 πΏπ. 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 β = β10π‘! + π£π‘ + π . 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 β1,0 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 β³ π½πΎπΏ? F T and K G L and Q H J and R J S and K 12. For π₯ β 3, !!!!
!!!= ?
A π₯ + 9 B π₯ + 3 C π₯ D 3 13. In β³ πππ, ππ½ = 9,ππ½ = 3,ππ = 18. Find the length of SV. 14. Find the coordinates of the centroid of the triangle with the given vertices.
π 5,7 ,π 9,β3 ,π(13,2)
14, 16, 18, 22, 24 15. Find the coordinates of the orthocenter of the triangle with the given vertices.
π β4,8 , π β1,5 ,π(5,5)
16. Identify each segment π΅π· as an altitude, median, or perpendicular bisector.
a.
b.
17. Complete the statement for β³ π ππ for medians π π, ππΏ, and ππΎ, and centroid J
π½π = π₯(ππΎ) 18. If πΈπΆ is an altitude of β³ π΄πΈπ·, πβ 1 = 2π₯ + 7, and πβ 2 = 3π₯ + 13, find πβ 1 and πβ 2.
32, 37 19. Write an algebraic proof. Given: β³ πππ,with medians ππ ,ππ,ππ Prove: πβ 1+πβ 2 = πβ 6+πβ 7
Statements Reasons
20. The lunch lady says that based on the figure provided, !
!π΄π = π΄π·. 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, πΊπ» β π»π½. Which must be true? A πΉπ½ is an altitude of β³ πΉπΊπ». B πΉπ½ is an angle bisector of β³ πΉπΊπ». C πΉπ½ is a median of β³ πΉπΊπ». D πΉπ½ is a perpendicular bisector of β³ πΉπΊπ». 22. What is the x-intercept of the graph 4π₯ β 6π¦ = 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
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