mrs. rivas (5-1) algebra find the value of x. 1

Mrs. Rivas

Homework

(5-1) Algebra Find the value of x.

𝟐(𝟐 𝒙+𝟏)=𝟏𝟖𝟒 𝒙+𝟐=𝟏𝟖

𝟒 𝒙=𝟏𝟔𝒙=𝟒

1.

Mrs. Rivas

Homework

(5-1) Algebra Find the value of x.

𝟐(𝟑 𝒙 )=𝟑𝟎𝟔 𝒙=𝟑𝟎𝒙=𝟓

2.

Mrs. Rivas

Homework

(5-1) Algebra Find the value of x.

3.

𝟐(𝟑 𝒙 )=𝟐𝟏𝟔 𝒙=𝟐𝟏𝒙=𝟑 .𝟓

Mrs. Rivas

Homework

X is the midpoint of . Y is the midpoint of .

4. Find XZ.

𝟗

Mrs. Rivas

Homework

X is the midpoint of . Y is the midpoint of .

5. If XY = 10, find MO.

𝟐𝟎

Mrs. Rivas

Homework

X is the midpoint of . Y is the midpoint of .

6. If is , find .

𝟔𝟒

𝟔𝟒

Mrs. Rivas

Homework

Use the diagram at the right for Exercises 7 and 8.

7. What is the distance across the lake?

𝟓 .𝟓

Mrs. Rivas

Homework

Use the diagram at the right for Exercises 7 and 8.

8. Is it a shorter distance from A to B or from B to C? Explain.

𝟓 .𝟓𝟒

BC is shorter. BC is half od 8 and AB is half od 11.

Mrs. Rivas

Homework

(5-2) Algebra Find the indicated variables and measures.

10. x, EH, EF

𝟓 𝒙+𝟑=𝟕 𝒙−𝟏𝟓 𝒙 𝟓 𝒙

𝟑=𝟐 𝒙−𝟏+𝟏+𝟏

𝟒=𝟐 𝒙𝟐=𝒙

𝑬𝑯=𝟓𝒙+𝟑=𝟓 (𝟐 )+𝟑=𝟏𝟑

𝑬𝑭=𝟕 𝒙−𝟏=𝟕 (𝟐 )−𝟏=𝟏𝟑

Mrs. Rivas

Homework

(5-2) Algebra Find the indicated variables and measures.

11. x, mTPS, mRPS

𝟐 𝒙 –𝟔=𝟑 𝒙 –𝟐𝟓𝟐 𝒙 𝟐 𝒙–𝟔=𝒙 –𝟐𝟓

+𝟐𝟓+𝟐𝟓𝟏𝟗=𝒙

𝒎∠𝑻𝑷𝑺=𝟐 𝒙−𝟔=𝟐 (𝟏𝟗)−𝟔=𝟑𝟐

𝒎∠𝑹𝑷𝑺=𝟑𝒙 −𝟐𝟓=𝟑 (𝟏𝟗)−𝟐𝟓=𝟑𝟐

Mrs. Rivas

Homework

(5-2) Algebra Find the indicated variables and measures.

12. a, b

𝟑𝒂 –𝟐=𝒂+𝟏𝟎

𝟑𝒃 –𝟏𝟓=𝟐𝒃+𝟓

𝟐𝒂 –𝟐=𝟏𝟎𝟐𝒂=𝟏𝟐𝒂=𝟔

𝒃 –𝟏𝟓=𝟓𝒃=𝟐𝟎

1.

Mrs. Rivas

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Mrs. Rivas

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2.

3.

Mrs. Rivas

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Mrs. Rivas

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4.

Mrs. Rivas

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5.

Mrs. Rivas

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6.

Mrs. Rivas

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7.

Mrs. Rivas

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𝒙+𝟓=𝟑𝒙+𝟕8.

−𝟐 𝒙+𝟓=𝟕−𝟐 𝒙=𝟐

𝒙=−𝟏

Mrs. Rivas

Homework

𝒙+𝟐=𝟐𝒙 –𝟑9.

−𝒙+𝟐=–𝟑−𝒙=–𝟓𝒙=𝟓

Mrs. Rivas

Homework

𝟓 𝒙+𝟕=𝒙+𝟖10.

𝟒 𝒙+𝟕=𝟖𝟒 𝒙=𝟏

𝒙=𝟏𝟒

Mrs. Rivas

Homework

(5-4) In ∆ABC, X is the centroid.

11. If CW = 15, find CX and XW.

𝟏𝟓𝑪𝑿=𝟐𝟑𝑪𝑾

𝑪𝑿=𝟐𝟑

(𝟏𝟓)

𝑪𝑿=𝟑𝟎𝟑

𝑪𝑿=𝟏𝟎

𝑿𝑾=𝑪𝑾 −𝑪𝑿

𝑿𝑾=𝟏𝟓−𝟏𝟎𝑿𝑾=𝟓

Mrs. Rivas

Homework

(5-4) In ∆ABC, X is the centroid.

12. If BX = 8, find BY and XY.

𝟖𝑩𝑿=𝟐𝟑𝑩𝒀

𝟖=𝟐𝟑𝑩𝒀

(𝟑𝟐 )𝟖=𝟐𝟑𝑩𝒀 (𝟑𝟐 )

𝟐𝟒𝟐

=𝑩𝒀

𝟏𝟐=𝑩𝒀

𝟏𝟐

𝑿𝒀=𝑩𝒀 −𝑩𝑿𝑿𝒀=𝟏𝟐−𝟖𝑿𝑾=𝟒

Mrs. Rivas

Homework

(5-4) In ∆ABC, X is the centroid.

13. If XZ = 3, find AX and AZ.

𝑿𝒁=𝟏𝟑𝑨𝒁

𝟑𝟑=

𝟏𝟑𝑨𝒁

(𝟑𝟏 )𝟑=𝟏𝟑𝑨𝒁 (𝟑𝟏 )

𝟗=𝑨𝒁

𝟗

𝑨𝑿=𝑨𝒁−𝑿𝒁𝑨𝑿=𝟗−𝟑𝑨𝑿=𝟔

Mrs. Rivas

Homework

Is a median, an altitude, or neither? Explain.

14. 15.

Median; bisects the opposite side.

Altitude; is perpendicular to the opposite side.

Mrs. Rivas

Homework

Is a median, an altitude, or neither? Explain.

16. 17.

Altitude; is perpendicular to the opposite side.

Neither; is not perpendicular to nor does it bisect the opposite side.

Mrs. Rivas

Homework

In Exercises 18–22, name each segment.

18. a median in ∆ABC

𝑪𝑱

Mrs. Rivas

Homework

In Exercises 18–22, name each segment.

19. an altitude for ∆ABC

𝑨𝑯

Mrs. Rivas

Homework

In Exercises 18–22, name each segment.

20. a median in ∆AHC

𝑰𝑯

Mrs. Rivas

Homework

In Exercises 18–22, name each segment.

21. an altitude for ∆AHB

𝑨𝑯

Mrs. Rivas

Homework

In Exercises 18–22, name each segment.

22. an altitude for ∆AHG.

𝑨𝑯

Mrs. Rivas

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23. A(0, 0), B(0, 2), C(3, 0). Find the orthocenter of ABC.

Mrs. Rivas

Homework

24. In which kind of triangle is the centroid at the same point as the orthocenter?

equilateral

Mrs. Rivas

Homework

𝑴𝒆𝒅𝒊𝒂𝒏 𝑪𝒆𝒏𝒕𝒓𝒐𝒊𝒅

𝑰𝒏𝒄𝒆𝒏𝒕𝒆𝒓 𝑪𝒐𝒏𝒄𝒖𝒓𝒓𝒆𝒏𝒕 𝒍𝒊𝒏𝒆𝒔 𝑪𝒊𝒓𝒄𝒖𝒎𝒄𝒆𝒏𝒕𝒆𝒓

𝑨𝒍𝒕𝒊𝒕𝒖𝒕𝒆 𝑶𝒓𝒕𝒉𝒐𝒄𝒆𝒏𝒕𝒆𝒓 𝑽𝒆𝒓𝒕𝒆𝒙