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Mrs. Rivas

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Presentation on theme: "Mrs. Rivas "β€” Presentation transcript:

1 Mrs. Rivas 𝟐(πŸπ’™ + 𝟏) = πŸπŸ– πŸ’π’™ + 𝟐 = πŸπŸ– πŸ’π’™ = πŸπŸ” 𝒙 = πŸ’
(5-1) Algebra Find the value of x. 1. 𝟐(πŸπ’™ + 𝟏) = πŸπŸ– πŸ’π’™ + 𝟐 = πŸπŸ– πŸ’π’™ = πŸπŸ” 𝒙 = πŸ’

2 Mrs. Rivas 𝟐(πŸ‘π’™) = πŸ‘πŸŽ πŸ”π’™ = πŸ‘πŸŽ 𝒙 = πŸ“ (5-1) Algebra Find the value of x.
2. 𝟐(πŸ‘π’™) = πŸ‘πŸŽ πŸ”π’™ = πŸ‘πŸŽ 𝒙 = πŸ“

3 Mrs. Rivas (5-1) Algebra Find the value of x. 3. 𝟐(πŸ‘π’™) = 𝟐𝟏 πŸ”π’™ = 𝟐𝟏 𝒙 = πŸ‘.πŸ“

4 Mrs. Rivas πŸ— X is the midpoint of 𝑴𝑡 . Y is the midpoint of 𝑢𝑡 .
4. Find XZ. πŸ—

5 Mrs. Rivas 𝟐𝟎 X is the midpoint of 𝑴𝑡 . Y is the midpoint of 𝑢𝑡 .
5. If XY = 10, find MO. 𝟐𝟎

6 Mrs. Rivas πŸ”πŸ’ πŸ”πŸ’ X is the midpoint of 𝑴𝑡 . Y is the midpoint of 𝑢𝑡 .
6. If π‘šοƒπ‘€ is 64, find π‘šοƒπ‘Œ. πŸ”πŸ’ πŸ”πŸ’

7 Mrs. Rivas πŸ“.πŸ“ Use the diagram at the right for Exercises 7 and 8.
7. What is the distance across the lake? πŸ“.πŸ“

8 Mrs. Rivas πŸ’ πŸ“.πŸ“ BC is shorter. BC is half od 8 and AB is half od 11.
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. πŸ’ BC is shorter. BC is half od 8 and AB is half od 11. πŸ“.πŸ“

9 Mrs. Rivas πŸ“π’™ + πŸ‘ = πŸ•π’™ βˆ’ 𝟏 ο€­πŸ“π’™ ο€­πŸ“π’™ πŸ‘ = πŸπ’™ βˆ’ 𝟏 + 𝟏 + 𝟏 πŸ’ = πŸπ’™ 𝟐 = 𝒙
(5-2) Algebra Find the indicated variables and measures. 10. x, EH, EF πŸ“π’™ + πŸ‘ = πŸ•π’™ βˆ’ 𝟏 ο€­πŸ“π’™ ο€­πŸ“π’™ πŸ‘ = πŸπ’™ βˆ’ 𝟏 + 𝟏 + 𝟏 πŸ’ = πŸπ’™ 𝟐 = 𝒙 𝑬𝑯=πŸ“π’™+πŸ‘=πŸ“ 𝟐 +πŸ‘=πŸπŸ‘ 𝑬𝑭=πŸ•π’™βˆ’πŸ=πŸ• 𝟐 βˆ’πŸ=πŸπŸ‘

10 Mrs. Rivas πŸπ’™ – πŸ” = πŸ‘π’™ – πŸπŸ“ ο€­πŸπ’™ ο€­πŸπ’™ – πŸ” = 𝒙 – πŸπŸ“ + πŸπŸ“ + πŸπŸ“ πŸπŸ— = 𝒙
(5-2) Algebra Find the indicated variables and measures. 11. x, mTPS, mRPS πŸπ’™ – πŸ” = πŸ‘π’™ – πŸπŸ“ ο€­πŸπ’™ ο€­πŸπ’™ – πŸ” = 𝒙 – πŸπŸ“ + πŸπŸ“ + πŸπŸ“ πŸπŸ— = 𝒙 π’Žβˆ π‘»π‘·π‘Ί=πŸπ’™βˆ’πŸ”=𝟐 πŸπŸ— βˆ’πŸ”=πŸ‘πŸ π’Žβˆ π‘Ήπ‘·π‘Ί=πŸ‘π’™βˆ’πŸπŸ“=πŸ‘ πŸπŸ— βˆ’πŸπŸ“=πŸ‘πŸ

11 Mrs. Rivas πŸ‘π’‚ – 𝟐 = 𝒂 + 𝟏𝟎 πŸπ’‚ – 𝟐 = 𝟏𝟎 πŸπ’‚ = 𝟏𝟐 𝒂 = πŸ” πŸ‘π’ƒ – πŸπŸ“ = πŸπ’ƒ + πŸ“
(5-2) Algebra Find the indicated variables and measures. 12. a, b πŸ‘π’‚ – 𝟐 = 𝒂 + 𝟏𝟎 πŸπ’‚ – 𝟐 = 𝟏𝟎 πŸπ’‚ = 𝟏𝟐 𝒂 = πŸ” πŸ‘π’ƒ – πŸπŸ“ = πŸπ’ƒ + πŸ“ 𝒃 – πŸπŸ“ = πŸ“ 𝒃 =𝟐𝟎

12 Mrs. Rivas 1.

13 Mrs. Rivas 2.

14 Mrs. Rivas 3.

15 Mrs. Rivas 4.

16 Mrs. Rivas 5.

17 Mrs. Rivas 6.

18 Mrs. Rivas 7.

19 Mrs. Rivas 𝒙 + πŸ“ = πŸ‘π’™ + πŸ• 8. βˆ’πŸπ’™ + πŸ“ = πŸ• βˆ’πŸπ’™ =𝟐 𝒙=βˆ’πŸ

20 Mrs. Rivas 𝒙 + 𝟐 = πŸπ’™ – πŸ‘ 9. βˆ’π’™ + 𝟐 = – πŸ‘ βˆ’π’™ = β€“πŸ“ 𝒙 = πŸ“

21 Mrs. Rivas 10. πŸ“π’™ + πŸ• = 𝒙 + πŸ– πŸ’π’™ + πŸ• = πŸ– πŸ’π’™ =𝟏 𝒙 = 𝟏 πŸ’

22 Mrs. Rivas π‘ͺ𝑿= 𝟐 πŸ‘ π‘ͺ𝑾 π‘ͺ𝑿= 𝟐 πŸ‘ (πŸπŸ“) 𝑿𝑾=π‘ͺπ‘Ύβˆ’π‘ͺ𝑿 π‘ͺ𝑿= πŸ‘πŸŽ πŸ‘ 𝑿𝑾=πŸπŸ“βˆ’πŸπŸŽ 𝑿𝑾=πŸ“
(5-4) In βˆ†ABC, X is the centroid. 11. If CW = 15, find CX and XW. π‘ͺ𝑿= 𝟐 πŸ‘ π‘ͺ𝑾 πŸπŸ“ π‘ͺ𝑿= 𝟐 πŸ‘ (πŸπŸ“) 𝑿𝑾=π‘ͺπ‘Ύβˆ’π‘ͺ𝑿 π‘ͺ𝑿= πŸ‘πŸŽ πŸ‘ 𝑿𝑾=πŸπŸ“βˆ’πŸπŸŽ 𝑿𝑾=πŸ“ π‘ͺ𝑿=𝟏𝟎

23 Mrs. Rivas 𝑩𝑿= 𝟐 πŸ‘ 𝑩𝒀 πŸ–= 𝟐 πŸ‘ 𝑩𝒀 𝑿𝒀=π‘©π’€βˆ’π‘©π‘Ώ πŸ‘ 𝟐 πŸ–= 𝟐 πŸ‘ 𝑩𝒀 πŸ‘ 𝟐 𝑿𝒀=πŸπŸβˆ’πŸ–
(5-4) In βˆ†ABC, X is the centroid. 12. If BX = 8, find BY and XY. 𝑩𝑿= 𝟐 πŸ‘ 𝑩𝒀 πŸ– 𝟏𝟐 πŸ–= 𝟐 πŸ‘ 𝑩𝒀 πŸ‘ 𝟐 πŸ–= 𝟐 πŸ‘ 𝑩𝒀 πŸ‘ 𝟐 𝑿𝒀=π‘©π’€βˆ’π‘©π‘Ώ 𝑿𝒀=πŸπŸβˆ’πŸ– πŸπŸ’ 𝟐 =𝑩𝒀 𝑿𝑾=πŸ’ 𝟏𝟐=𝑩𝒀

24 Mrs. Rivas 𝑿𝒁= 𝟏 πŸ‘ 𝑨𝒁 πŸ‘= 𝟏 πŸ‘ 𝑨𝒁 πŸ‘ 𝟏 πŸ‘= 𝟏 πŸ‘ 𝑨𝒁 πŸ‘ 𝟏 𝑨𝑿=π‘¨π’βˆ’π‘Ώπ’ 𝑨𝑿=πŸ—βˆ’πŸ‘ πŸ—=𝑨𝒁
(5-4) In βˆ†ABC, X is the centroid. 13. If XZ = 3, find AX and AZ. 𝑿𝒁= 𝟏 πŸ‘ 𝑨𝒁 πŸ— πŸ‘ πŸ‘= 𝟏 πŸ‘ 𝑨𝒁 πŸ‘ 𝟏 πŸ‘= 𝟏 πŸ‘ 𝑨𝒁 πŸ‘ 𝟏 𝑨𝑿=π‘¨π’βˆ’π‘Ώπ’ 𝑨𝑿=πŸ—βˆ’πŸ‘ πŸ—=𝑨𝒁 𝑨𝑿=πŸ”

25 Mrs. Rivas Is 𝑨𝑩 a median, an altitude, or neither? Explain. 15. 14.
Altitude; 𝑨𝑩 is perpendicular to the opposite side. Median; 𝑨𝑩 bisects the opposite side.

26 Mrs. Rivas Is 𝑨𝑩 a median, an altitude, or neither? Explain. 17. 16.
Altitude; 𝑨𝑩 is perpendicular to the opposite side. Neither; 𝑨𝑩 is not perpendicular to nor does it bisect the opposite side.

27 Mrs. Rivas π‘ͺ𝑱 In Exercises 18–22, name each segment.
18. a median in βˆ†ABC π‘ͺ𝑱

28 Mrs. Rivas 𝑨𝑯 In Exercises 18–22, name each segment.
19. an altitude for βˆ†ABC 𝑨𝑯

29 Mrs. Rivas 𝑰𝑯 In Exercises 18–22, name each segment.
20. a median in βˆ†AHC 𝑰𝑯

30 Mrs. Rivas 𝑨𝑯 In Exercises 18–22, name each segment.
21. an altitude for βˆ†AHB 𝑨𝑯

31 Mrs. Rivas 𝑨𝑯 In Exercises 18–22, name each segment.
22. an altitude for βˆ†AHG. 𝑨𝑯

32 Mrs. Rivas 23. A(0, 0), B(0, ο€­2), C(ο€­3, 0). Find the orthocenter of βˆ†ABC.

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

34 Mrs. Rivas π‘΄π’†π’…π’Šπ’‚π’ π‘·π’π’Šπ’π’• 𝒐𝒇 π’„π’π’π’„π’–π’“π’“π’†π’π’„π’š π‘ͺπ’†π’π’•π’“π’π’Šπ’… 𝑰𝒏𝒄𝒆𝒏𝒕𝒆𝒓
π‘ͺ𝒐𝒏𝒄𝒖𝒓𝒓𝒆𝒏𝒕 π’π’Šπ’π’†π’” π‘ͺπ’Šπ’“π’„π’–π’Žπ’„π’†π’π’•π’†π’“ π‘¨π’π’•π’Šπ’•π’–π’•π’† 𝑢𝒓𝒕𝒉𝒐𝒄𝒆𝒏𝒕𝒆𝒓 𝑽𝒆𝒓𝒕𝒆𝒙


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