Mrs. Rivasc Perfect Practice Lesson 5-1 𝟐(𝟕𝒙−𝟏)=𝟒𝟖 𝟏𝟒𝒙−𝟐=𝟒𝟖 𝟏𝟒𝒙=𝟓𝟎 Find the value of x. 1. 𝟐(𝟕𝒙−𝟏)=𝟒𝟖 𝟏𝟒𝒙−𝟐=𝟒𝟖 𝟏𝟒𝒙=𝟓𝟎 𝒙= 𝟓𝟎 𝟏𝟒 𝒙= 𝟐𝟓 𝟕

Mrs. Rivas Perfect Practice 𝟐(𝟒𝟖)=𝟑𝒙 𝟗𝟔=𝟑𝒙 𝟑𝟐=𝒙 Lesson 5-1 Find the value of x. 2. 𝟐(𝟒𝟖)=𝟑𝒙 𝟗𝟔=𝟑𝒙 𝟑𝟐=𝒙

Mrs. Rivas Perfect Practice 𝟐𝒙=𝟏𝟒 𝒙=𝟕 Lesson 5-1 Find the value of x. 3. 𝟐𝒙=𝟏𝟒 𝒙=𝟕

Mrs. Rivas Perfect Practice 𝑳𝑴 ∥ 𝑹𝑺 𝑴𝑵 ∥ 𝑸𝑹 𝑳𝑵 ∥ 𝑸𝑺 Lesson 5-1 In the figure at the right, points Q, R, and S are midpoints of LMN. 4. Identify all pairs of parallel segments. 𝑳𝑴 ∥ 𝑹𝑺 𝑴𝑵 ∥ 𝑸𝑹 𝑳𝑵 ∥ 𝑸𝑺

Mrs. Rivas Perfect Practice 𝑸𝑺 =𝟐𝟓 Lesson 5-1 In the figure at the right, points Q, R, and S are midpoints of LMN. 𝑸𝑺 =𝟐𝟓

Mrs. Rivas Perfect Practice 𝑸𝑹 =𝟐𝟎 Lesson 5-1 In the figure at the right, points Q, R, and S are midpoints of LMN. 𝑸𝑹 =𝟐𝟎

Mrs. Rivas Perfect Practice 𝒎∠𝑺𝑸𝑴=𝟓𝟑 Lesson 5-1 In the figure at the right, points Q, R, and S are midpoints of LMN. 𝒎∠𝑺𝑸𝑴=𝟓𝟑

Mrs. Rivas Perfect Practice 𝟏𝟒𝟎 𝒇𝒕 Lesson 5-1 𝟐𝟖𝟎 𝟐 8. A sinkhole caused the sudden collapse of a large section of highway. Highway safety investigators paced out the triangle shown in the figure to help them estimate the distance across the sinkhole. What is the distance across the sinkhole? 𝟐𝟖𝟎 𝟐 𝟏𝟒𝟎 𝒇𝒕

Mrs. Rivas Perfect Practice Lesson 5-2 𝟐𝒙−𝟑=𝒙+𝟐 𝒙−𝟑=𝟐 𝒙=𝟓 Use the figure at the right for Exercises 9–12. 9. Find the value of x. 𝟐𝒙−𝟑=𝒙+𝟐 𝒙−𝟑=𝟐 𝒙=𝟓

Mrs. Rivas Perfect Practice Lesson 5-2 𝑨𝑫 =𝟐𝒙−𝟑 =𝟐(𝟓)−𝟑 =𝟏𝟎−𝟑 𝑨𝑫 =𝟕 Use the figure at the right for Exercises 9–12. 𝑨𝑫 =𝟐𝒙−𝟑 =𝟐(𝟓)−𝟑 =𝟏𝟎−𝟑 𝑨𝑫 =𝟕

Mrs. Rivas Perfect Practice Lesson 5-2 𝒚+𝟓=𝟑𝒚 𝟓=𝟐𝒚 𝟓 𝟐 =𝒚 Use the figure at the right for Exercises 9–12. 𝒚+𝟓=𝟑𝒚 𝟓=𝟐𝒚 𝟓 𝟐 =𝒚

Mrs. Rivas Perfect Practice Lesson 5-2 𝑬𝑮 =𝒚+𝟓 𝑬𝑮 = 𝟓 𝟐 +𝟓 𝑬𝑮 = 𝟏𝟓 𝟐 Use the figure at the right for Exercises 9–12. 𝑬𝑮 =𝒚+𝟓 𝑬𝑮 = 𝟓 𝟐 +𝟓 𝑬𝑮 = 𝟏𝟓 𝟐

Mrs. Rivas Perfect Practice Lesson 5-2 𝒚− 𝒚 𝟏 =𝒎(𝒙− 𝒙 𝟏 ) 13. Find an equation in slope-intercept form for the perpendicular bisector of the segment with endpoints H(–3, 2) and K(7, –5). 𝒙 𝟏 , 𝒚 𝟏 𝒙 𝟐 , 𝒚 𝟐 𝒎= 𝒚 𝟐 − 𝒚 𝟏 𝒙 𝟐 − 𝒙 𝟏 = −𝟓−𝟐 𝟕−(−𝟑) =− 𝟕 𝟏𝟎 𝑃𝑒𝑟𝑝𝑒𝑛𝑑𝑖𝑐𝑢𝑙𝑎𝑟 𝒎= 𝟏𝟎 𝟕 ① ② 𝒚− 𝒚 𝟏 =𝒎(𝒙− 𝒙 𝟏 ) ④ 𝒎= 𝒙 𝟏 + 𝒙 𝟐 𝟐 , 𝒚 𝟐 + 𝒚 𝟏 𝟐 ③ 𝒚− − 𝟑 𝟐 = 𝟏𝟎 𝟕 (𝒙−𝟐) 𝒎= −𝟑+𝟕 𝟐 , −𝟓+𝟐 𝟐 𝒚+ 𝟑 𝟐 = 𝟏𝟎 𝟕 𝒙− 𝟐𝟎 𝟕 𝒎= 𝟐,− 𝟑 𝟐 𝒚= 𝟏𝟎 𝟕 𝒙− 𝟔𝟏 𝟏𝟒 𝒙 𝟏 , 𝒚 𝟏

Mrs. Rivas Perfect Practice 𝑪 Lesson 5-3 Use the figure at the right for Exercises 14 and 15. 14. What is the point of concurrency of the angle bisectors of QRS? 𝑪

Mrs. Rivas Perfect Practice Lesson 5-3 𝟐𝒙+𝟑=𝟓−𝟒(𝒙+𝟏) 𝟐𝒙+𝟑=𝟓−𝟒𝒙+𝟒 Use the figure at the right for Exercises 14 and 15. 𝟐𝒙+𝟑=𝟓−𝟒(𝒙+𝟏) 𝟐𝒙+𝟑=𝟓−𝟒𝒙+𝟒 𝟐𝒙+𝟑=𝟏−𝟒𝒙 𝟔𝒙+𝟑=𝟏 𝟔𝒙=−𝟐 𝒙=− 𝟐 𝟔 𝒙=− 𝟏 𝟑

Mrs. Rivas Perfect Practice Lesson 5-4 𝑯𝑳= 𝟏 𝟑 𝑯𝑭 𝟑𝟎= 𝟏 𝟑 𝑯𝑭 𝑳𝑭=𝑯𝑭−𝑯𝑳 In DEF, L is the centroid. 16. If HL = 30, find LF and HF. 𝑯𝑳= 𝟏 𝟑 𝑯𝑭 𝟑𝟎= 𝟏 𝟑 𝑯𝑭 𝑳𝑭=𝑯𝑭−𝑯𝑳 𝟑 𝟏 𝟑𝟎= 𝟏 𝟑 𝑯𝑭 𝟑 𝟏 𝑳𝑭=𝟗𝟎−𝟑𝟎 𝑳𝑭=𝟔𝟎 𝟗𝟎=𝑯𝑭

Mrs. Rivas Perfect Practice Lesson 5-4 𝑳𝑬= 𝟐 𝟑 𝑲𝑬 𝑳𝑬= 𝟐 𝟑 (𝟏𝟓) In DEF, L is the centroid. 17. If KE = 15, find KL and LE. 𝑳𝑬= 𝟐 𝟑 𝑲𝑬 𝑳𝑬= 𝟐 𝟑 (𝟏𝟓) 𝑲𝑳=𝑲𝑬−𝑳𝑬 𝑳𝑬= 𝟑𝟎 𝟑 𝑲𝑳=𝟏𝟓−𝟏𝟎 𝑲𝑳=𝟓 𝑳𝑬=𝟏𝟎

Mrs. Rivas Perfect Practice Lesson 5-4 𝑫𝑳= 𝟐 𝟑 𝑫𝑱 𝟐𝟒= 𝟐 𝟑 𝑩𝒀 𝑳𝑱=𝑩𝒀−𝑫𝑳 In DEF, L is the centroid. 18. If DL = 24, find LJ and DJ. 𝑫𝑳= 𝟐 𝟑 𝑫𝑱 𝟐𝟒= 𝟐 𝟑 𝑩𝒀 𝟑 𝟐 𝟐𝟒= 𝟐 𝟑 𝑩𝒀 𝟑 𝟐 𝑳𝑱=𝑩𝒀−𝑫𝑳 𝑳𝑱=𝟑𝟔−𝟐𝟒 𝟕𝟐 𝟐 =𝑩𝒀 𝑳𝑱=𝟏𝟐 𝟑𝟔=𝑩𝒀

Mrs. Rivas Perfect Practice Lesson 5-4 Median; the line intersects Is 𝑨𝑩 a median, an altitude, a perpendicular bisector, or none of these? How do you know? 19. Median; the line intersects A and bisects a side at B.

Mrs. Rivas Perfect Practice Lesson 5-4 Is 𝑨𝑩 a median, an altitude, a perpendicular bisector, or none of these? How do you know? 20. Altitude; the segment intersects A and is  to a side at B.

Mrs. Rivas Perfect Practice Lesson 5-4 Is 𝑨𝑩 a median, an altitude, a perpendicular bisector, or none of these? How do you know? 21.  bisector; the segment is perpendicular to and bisects a side at B, but it does not intersect a vertex.

Mrs. Rivas Perfect Practice Lesson 5-4 line k 22. Tell which line contains each point for ∆ABC. a. the circumcenter line k

Mrs. Rivas Perfect Practice Lesson 5-4 line m 22. Tell which line contains each point for ∆ABC. b. the orthocenter line m

Mrs. Rivas Perfect Practice Lesson 5-4 line ℓ 22. Tell which line contains each point for ∆ABC. c. the centroid line ℓ

Mrs. Rivas Perfect Practice Lesson 5-4 line n 22. Tell which line contains each point for ∆ABC. d. the incenter line n

Mrs. Rivas Perfect Practice Lesson 5-6 No; 2+ 3 ≯ 5. Can a triangle have sides with the given lengths? Explain. 23. 2 in., 3 in., 5 in. No; 2+ 3 ≯ 5.

Mrs. Rivas Perfect Practice Lesson 5-6 Can a triangle have sides with the given lengths? Explain. 24. 9 cm, 11 cm, 15 cm 𝟗+𝟏𝟏>𝟏𝟓 𝟏𝟏+𝟏𝟓>𝟗 𝟏𝟓+𝟗>𝟏𝟏 𝟐𝟎>𝟏𝟓 𝟐𝟔>𝟗 𝟐𝟒>𝟏𝟏 𝒚𝒆𝒔 𝒚𝒆𝒔 𝒚𝒆𝒔

Mrs. Rivas Perfect Practice 𝑹𝑵 , 𝑹𝑺 , 𝑵𝑺 Lesson 5-6 List the sides of each triangle in order from shortest to longest. 25. 𝑹𝑵 , 𝑹𝑺 , 𝑵𝑺

Mrs. Rivas Perfect Practice 𝑱𝑩 , 𝑷𝑩 , 𝑷𝑱 Lesson 5-6 List the sides of each triangle in order from shortest to longest. 26. 𝑱𝑩 , 𝑷𝑩 , 𝑷𝑱

Mrs. Rivas Perfect Practice 𝑴𝑸 , 𝑸𝑫 , 𝑴𝑫 Lesson 5-6 List the sides of each triangle in order from shortest to longest. 27. 𝑴𝑸 , 𝑸𝑫 , 𝑴𝑫