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 △ 𝐴𝐵𝐶. List the segment congruent to 𝐵𝐹. 3. Find each measure

a. ∠𝐷𝐵𝐴

b. XA c. PN

28, 30, 38, 46 4. Point P is the incenter of △ 𝐴𝐸𝐶. Find each measure.

a. DE

b. 𝑚∠𝐷𝐸𝑃 5. Write a two-column proof. Given: △ 𝐴𝐵𝐶, angle  bisectors  𝐴𝐷,𝐵𝐸, and  𝐶𝐹 𝐾𝑃 ⊥ 𝐴𝐵,𝐾𝑄 ⊥ 𝐵𝐶,𝐾𝑅 ⊥ 𝐴𝐶 Prove: 𝐾𝑃 = 𝐾𝑄 = 𝐾𝑅

Statements Reasons

6. Find the coordinates of the circumcenter of the triangles with the given vertices. Explain.

𝐽 5,0 ,𝐾 5,−8 , 𝐿(0,0)

48, 54, 55, 56 7. Brooke’s 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 𝐿𝑀. 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 ℎ = −10𝑡! + 𝑣𝑡 + 𝑠. 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 −1,0  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 △ 𝐽𝐾𝐿? F T and K G L and Q H J and R J S and K 12. For 𝑥 ≠ 3, !!!!

!!!=  ?

A 𝑥 + 9 B 𝑥 + 3 C 𝑥 D 3 13. In △ 𝑆𝑍𝑈, 𝑈𝐽 = 9,𝑉𝐽 = 3,𝑍𝑇 = 18. Find the length of SV. 14. Find the coordinates of the centroid of the triangle with the given vertices.

𝑋 5,7 ,𝑌 9,−3 ,𝑍(13,2)

14, 16, 18, 22, 24 15. Find the coordinates of the orthocenter of the triangle with the given vertices.

𝑅 −4,8 , 𝑆 −1,5 ,𝑇(5,5)

16. Identify each segment 𝐵𝐷 as an altitude, median, or perpendicular bisector.

a.

b.

17. Complete the statement for △ 𝑅𝑆𝑇 for medians 𝑅𝑀, 𝑆𝐿, and 𝑇𝐾, and centroid J

𝐽𝑇 = 𝑥(𝑇𝐾) 18. If 𝐸𝐶 is an altitude of △ 𝐴𝐸𝐷, 𝑚∠1 = 2𝑥 + 7, and 𝑚∠2 = 3𝑥 + 13,  find 𝑚∠1 and 𝑚∠2.

32, 37 19. Write an algebraic proof. Given: △ 𝑋𝑌𝑍,with  medians  𝑋𝑅,𝑌𝑆,𝑍𝑄 Prove:  𝑚∠1+𝑚∠2 = 𝑚∠6+𝑚∠7

Statements Reasons

20. The lunch lady says that based on the figure provided, !

!𝐴𝑃 = 𝐴𝐷. 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, 𝐺𝐻 ≅ 𝐻𝐽. Which must be true? A 𝐹𝐽 is an altitude of △ 𝐹𝐺𝐻. B 𝐹𝐽 is an angle bisector of △ 𝐹𝐺𝐻. C 𝐹𝐽 is a median of △ 𝐹𝐺𝐻. D 𝐹𝐽 is a perpendicular bisector of △ 𝐹𝐺𝐻. 22. What is the x-intercept of the graph 4𝑥 − 6𝑦 = 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