Mrs. Rivasc

Perfect PracticeLesson 5-1

Find the value of x.1. 𝟐(𝟕 𝒙−𝟏)=𝟒𝟖

𝟏𝟒𝒙−𝟐=𝟒𝟖𝟏𝟒𝒙=𝟓𝟎

𝒙=𝟓𝟎𝟏𝟒

𝒙=𝟐𝟓𝟕

Mrs. Rivas

Perfect PracticeLesson 5-1

Find the value of x.2. 𝟐(𝟒𝟖)=𝟑 𝒙

𝟗𝟔=𝟑 𝒙𝟑𝟐=𝒙

Mrs. Rivas

Perfect PracticeLesson 5-1

Find the value of x.3. 𝟐 𝒙=𝟏𝟒

𝒙=𝟕

Mrs. Rivas

Perfect Practice

In the figure at the right, points Q, R, and S are midpoints of LMN.4. Identify all pairs of parallel segments.

Lesson 5-1

𝑳𝑴 ∥𝑹𝑺𝑴𝑵 ∥𝑸𝑹𝑳𝑵 ∥𝑸𝑺

Mrs. Rivas

Perfect Practice

In the figure at the right, points Q, R, and S are midpoints of LMN.

Lesson 5-1

𝑸𝑺=𝟐𝟓

Mrs. Rivas

Perfect Practice

In the figure at the right, points Q, R, and S are midpoints of LMN.

Lesson 5-1

𝑸𝑹=𝟐𝟎

Mrs. Rivas

Perfect Practice

In the figure at the right, points Q, R, and S are midpoints of LMN.

Lesson 5-1

𝒎∠𝑺𝑸𝑴=𝟓𝟑

Mrs. Rivas

Perfect Practice

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?

Lesson 5-1

𝟐𝟖𝟎𝟐

𝟏𝟒𝟎 𝒇𝒕

Mrs. Rivas

Perfect PracticeLesson 5-2

Use the figure at the right for Exercises 9–12.

9. Find the value of x.

𝟐 𝒙−𝟑=𝒙+𝟐𝒙−𝟑=𝟐𝒙=𝟓

Mrs. Rivas

Perfect PracticeLesson 5-2

Use the figure at the right for Exercises 9–12.

𝑨𝑫=𝟐 𝒙−𝟑¿𝟐(𝟓)−𝟑

¿𝟏𝟎−𝟑𝑨𝑫=𝟕

Mrs. Rivas

Perfect PracticeLesson 5-2

Use the figure at the right for Exercises 9–12.

𝒚+𝟓=𝟑 𝒚𝟓=𝟐 𝒚𝟓𝟐

=𝒚

Mrs. Rivas

Perfect PracticeLesson 5-2

Use the figure at the right for Exercises 9–12.

𝑬𝑮=𝒚+𝟓𝑬𝑮=

𝟓𝟐

+𝟓

𝑬𝑮=𝟏𝟓𝟐

Mrs. Rivas

Perfect Practice

13. Find an equation in slope-intercept form for the perpendicular bisector of the segment with endpoints H(–3, 2) and K(7, –5).

Lesson 5-2

𝒙𝟏 , 𝒚𝟏 𝒙𝟐 , 𝒚𝟐

𝒚 −𝒚𝟏=𝒎(𝒙−𝒙𝟏)

𝒚 −(−𝟑𝟐 )=𝟏𝟎𝟕

(𝒙−𝟐)

𝒚+𝟑𝟐

=𝟏𝟎𝟕

𝒙−𝟐𝟎𝟕

𝒚=𝟏𝟎𝟕

𝒙−𝟔𝟏𝟏𝟒

𝒎=( 𝒙𝟏+𝒙𝟐

𝟐,𝒚𝟐+𝒚𝟏

𝟐 )𝒎=(−𝟑+𝟕

𝟐,−𝟓+𝟐𝟐 )

𝒎=(𝟐 ,−𝟑𝟐 )𝒙𝟏 , 𝒚𝟏

① ②

③④

Mrs. Rivas

Perfect PracticeLesson 5-3

14. What is the point of concurrency of the angle bisectors of QRS?

Use the figure at the right for Exercises 14 and 15.

𝑪

Mrs. Rivas

Perfect PracticeLesson 5-3

Use the figure at the right for Exercises 14 and 15.

𝟐 𝒙+𝟑=𝟓−𝟒(𝒙+𝟏)𝟐 𝒙+𝟑=𝟓−𝟒 𝒙+𝟒𝟐 𝒙+𝟑=𝟏−𝟒 𝒙𝟔 𝒙+𝟑=𝟏

𝟔 𝒙=−𝟐𝒙=−

𝟐𝟔 𝒙=−

𝟏𝟑

Mrs. Rivas

Perfect PracticeLesson 5-4

In DEF, L is the centroid.

16. If HL = 30, find LF and HF.

𝑯𝑳=𝟏𝟑𝑯𝑭

𝟑𝟎=𝟏𝟑𝑯𝑭

(𝟑𝟏 )𝟑𝟎=𝟏𝟑𝑯𝑭 (𝟑𝟏 )

𝟗𝟎=𝑯𝑭

𝑳𝑭=𝑯𝑭 −𝑯𝑳𝑳𝑭=𝟗𝟎−𝟑𝟎𝑳𝑭=𝟔𝟎

Mrs. Rivas

Perfect PracticeLesson 5-4

In DEF, L is the centroid.

17. If KE = 15, find KL and LE.

𝑳𝑬=𝟐𝟑𝑲𝑬

𝑳𝑬=𝟐𝟑

(𝟏𝟓)

𝑳𝑬=𝟑𝟎𝟑

𝑳𝑬=𝟏𝟎

𝑲𝑳=𝑲𝑬−𝑳𝑬𝑲𝑳=𝟏𝟓−𝟏𝟎𝑲𝑳=𝟓

Mrs. Rivas

Perfect PracticeLesson 5-4

In DEF, L is the centroid.

18. If DL = 24, find LJ and DJ.

𝑫𝑳=𝟐𝟑𝑫𝑱

𝟐𝟒=𝟐𝟑𝑩𝒀

(𝟑𝟐 )𝟐𝟒=𝟐𝟑𝑩𝒀 (𝟑𝟐 )

𝟕𝟐𝟐

=𝑩𝒀

𝟑𝟔=𝑩𝒀

𝑳𝑱=𝑩𝒀−𝑫𝑳𝑳𝑱=𝟑𝟔−𝟐𝟒𝑳𝑱=𝟏𝟐

Mrs. Rivas

Perfect PracticeLesson 5-4

Is 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 PracticeLesson 5-4

Is 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 PracticeLesson 5-4

Is 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 PracticeLesson 5-4

22. Tell which line contains each point for ∆ABC.a. the circumcenter

line k

Mrs. Rivas

Perfect PracticeLesson 5-4

22. Tell which line contains each point for ∆ABC.b. the orthocenter

line m

Mrs. Rivas

Perfect PracticeLesson 5-4

22. Tell which line contains each point for ∆ABC.c. the centroid

line ℓ

Mrs. Rivas

Perfect PracticeLesson 5-4

22. Tell which line contains each point for ∆ABC.

d. the incenter

line n

Mrs. Rivas

Perfect PracticeLesson 5-6

Can a triangle have sides with the given lengths? Explain.

23. 2 in., 3 in., 5 in.

No;

Mrs. Rivas

Perfect PracticeLesson 5-6

Can a triangle have sides with the given lengths? Explain.

24. 9 cm, 11 cm, 15 cm

𝟗+𝟏𝟏>𝟏𝟓𝟐𝟎>𝟏𝟓𝒚𝒆𝒔

𝟏𝟏+𝟏𝟓>𝟗𝟐𝟔>𝟗𝒚𝒆𝒔

𝟏𝟓+𝟗>𝟏𝟏𝟐𝟒>𝟏𝟏𝒚𝒆𝒔

Mrs. Rivas

Perfect PracticeLesson 5-6

List the sides of each triangle in order from shortest to longest.

25.

,

Mrs. Rivas

Perfect PracticeLesson 5-6

List the sides of each triangle in order from shortest to longest.

26.

,

Mrs. Rivas

Perfect PracticeLesson 5-6

List the sides of each triangle in order from shortest to longest.

27.

,