Slide 1

Homework

Mrs. Rivas

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

𝟐(𝟐𝒙 + 𝟏) = 𝟏𝟖
𝟒𝒙 + 𝟐 = 𝟏𝟖
𝟒𝒙 = 𝟏𝟔
𝒙 = 𝟒


Slide 2

Homework

Mrs. Rivas

(5-1) Algebra Find the value of x.
2.

𝟐(𝟑𝒙) = 𝟑𝟎
𝟔𝒙 = 𝟑𝟎
𝒙 = 𝟓


Slide 3

Homework

Mrs. Rivas

(5-1) Algebra Find the value of x.
3.

𝟐(𝟑𝒙) = 𝟐𝟏
𝟔𝒙 = 𝟐𝟏
𝒙 = 𝟑. 𝟓


Slide 4

Homework

Mrs. Rivas

X is the midpoint of 𝑴𝑵. Y is the midpoint of 𝑶𝑵.
4. Find XZ.

𝟗


Slide 5

Homework

Mrs. Rivas

X is the midpoint of 𝑴𝑵. Y is the midpoint of 𝑶𝑵.
5. If XY = 10, find MO.

𝟐𝟎


Slide 6

Homework

Mrs. Rivas

X is the midpoint of 𝑴𝑵. Y is the midpoint of 𝑶𝑵.
6. If 𝑚𝑀 is 64, find 𝑚𝑌 .

𝟔𝟒

𝟔𝟒


Slide 7

Homework

Mrs. Rivas

Use the diagram at the right for Exercises 7 and 8.
7. What is the distance across the lake?

𝟓. 𝟓


Slide 8

Homework

Mrs. Rivas

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.

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

𝟓. 𝟓

𝟒


Slide 9

Homework

Mrs. Rivas

(5-2) Algebra Find the indicated variables and measures.
10. x, EH, EF

𝟓𝒙 + 𝟑
𝟓𝒙
𝟑
+𝟏
𝟒
𝟐
𝑬𝑯 = 𝟓𝒙 + 𝟑 = 𝟓 𝟐 + 𝟑 = 𝟏𝟑
𝑬𝑭 = 𝟕𝒙 − 𝟏 = 𝟕 𝟐 − 𝟏 = 𝟏𝟑

= 𝟕𝒙 − 𝟏
𝟓𝒙
= 𝟐𝒙 − 𝟏
+𝟏
= 𝟐𝒙
= 𝒙


Slide 10

Homework

Mrs. Rivas

(5-2) Algebra Find the indicated variables and measures.
11. x, mTPS, mRPS

𝟐𝒙 – 𝟔 = 𝟑𝒙 – 𝟐𝟓
𝟐𝒙
𝟐𝒙
– 𝟔 = 𝒙 – 𝟐𝟓
+ 𝟐𝟓
+ 𝟐𝟓
𝟏𝟗 = 𝒙
𝒎∠𝑻𝑷𝑺 = 𝟐𝒙 − 𝟔 = 𝟐 𝟏𝟗 − 𝟔 = 𝟑𝟐
𝒎∠𝑹𝑷𝑺 = 𝟑𝒙 − 𝟐𝟓 = 𝟑 𝟏𝟗 − 𝟐𝟓 = 𝟑𝟐


Slide 11

Homework

Mrs. Rivas

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

12. a, b

𝟑𝒂 – 𝟐
𝟐𝒂 – 𝟐
𝟐𝒂
𝒂

=
=
=
=

𝒂 + 𝟏𝟎
𝟏𝟎
𝟏𝟐
𝟔

𝟑𝒃 – 𝟏𝟓 = 𝟐𝒃 + 𝟓
𝒃 – 𝟏𝟓 = 𝟓
𝒃 = 𝟐𝟎


Slide 12

Homework
1.

Mrs. Rivas


Slide 13

Homework
2.

Mrs. Rivas


Slide 14

Homework
3.

Mrs. Rivas


Slide 15

Homework
4.

Mrs. Rivas


Slide 16

Homework
5.

Mrs. Rivas


Slide 17

Homework
6.

Mrs. Rivas


Slide 18

Homework
7.

Mrs. Rivas


Slide 19

Homework
8.

Mrs. Rivas

𝒙 + 𝟓 = 𝟑𝒙 + 𝟕
−𝟐𝒙 + 𝟓 = 𝟕
−𝟐𝒙 = 𝟐
𝒙 = −𝟏


Slide 20

Homework
9.

Mrs. Rivas

𝒙 + 𝟐 = 𝟐𝒙 – 𝟑
−𝒙 + 𝟐 = – 𝟑
−𝒙 = – 𝟓
𝒙 = 𝟓


Slide 21

Homework
10.

Mrs. Rivas

𝟓𝒙 + 𝟕 = 𝒙 + 𝟖
𝟒𝒙 + 𝟕 = 𝟖
𝟒𝒙 = 𝟏
𝟏
𝒙 =
𝟒


Slide 22

Homework

Mrs. Rivas

(5-4) In ∆ABC, X is the centroid.
11. If CW = 15, find CX and XW.

𝟐
𝑪𝑿 = 𝑪𝑾
𝟑
𝟐
𝑪𝑿 = (𝟏𝟓)
𝟑
𝟑𝟎
𝑪𝑿 =
𝟑
𝑪𝑿 = 𝟏𝟎

𝟏𝟓

𝑿𝑾 = 𝑪𝑾 − 𝑪𝑿

𝑿𝑾 = 𝟏𝟓 − 𝟏𝟎
𝑿𝑾 = 𝟓


Slide 23

Homework

Mrs. Rivas

(5-4) In ∆ABC, X is the centroid.
12. If BX = 8, find BY and XY.

𝟐
𝑩𝑿 = 𝑩𝒀
𝟑
𝟐
𝟖 = 𝑩𝒀
𝟑
𝟑
𝟐
𝟑
𝟖 = 𝑩𝒀
𝟐
𝟑
𝟐
𝟐𝟒
= 𝑩𝒀
𝟐
𝟏𝟐 = 𝑩𝒀

𝟖

𝑿𝒀 = 𝑩𝒀 − 𝑩𝑿
𝑿𝒀 = 𝟏𝟐 − 𝟖
𝑿𝑾 = 𝟒

𝟏𝟐


Slide 24

Homework

Mrs. Rivas

(5-4) In ∆ABC, X is the centroid.
13. If XZ = 3, find AX and AZ.

𝟏
𝑿𝒁 = 𝑨𝒁
𝟑
𝟏
𝟑 = 𝑨𝒁
𝟑
𝟑
𝟏
𝟑
𝟑 = 𝑨𝒁
𝟏
𝟑
𝟏
𝟗 = 𝑨𝒁

𝟗
𝟑

𝑨𝑿 = 𝑨𝒁 − 𝑿𝒁
𝑨𝑿 = 𝟗 − 𝟑
𝑨𝑿 = 𝟔


Slide 25

Homework

Mrs. Rivas

Is 𝑨𝑩 a median, an altitude, or neither? Explain.
15.

14.

Median; 𝑨𝑩 bisects
the opposite side.

Altitude; 𝑨𝑩 is
perpendicular to the
opposite side.


Slide 26

Homework

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.


Slide 27

Homework
In Exercises 18–22, name each segment.
18. a median in ∆ABC

𝑪𝑱

Mrs. Rivas


Slide 28

Homework
In Exercises 18–22, name each segment.
19. an altitude for ∆ABC

𝑨𝑯

Mrs. Rivas


Slide 29

Homework
In Exercises 18–22, name each segment.
20. a median in ∆AHC

𝑰𝑯

Mrs. Rivas


Slide 30

Homework
In Exercises 18–22, name each segment.
21. an altitude for ∆AHB

𝑨𝑯

Mrs. Rivas


Slide 31

Homework
In Exercises 18–22, name each segment.
22. an altitude for ∆AHG.

𝑨𝑯

Mrs. Rivas


Slide 32

Homework

Mrs. Rivas

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


Slide 33

Homework

Mrs. Rivas

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

equilateral


Slide 34

Homework

𝑴𝒆𝒅𝒊𝒂𝒏

𝑰𝒏𝒄𝒆𝒏𝒕𝒆𝒓

𝑨𝒍𝒕𝒊𝒕𝒖𝒕𝒆

𝑷𝒐𝒊𝒏𝒕 𝒐𝒇
𝒄𝒐𝒏𝒄𝒖𝒓𝒓𝒆𝒏𝒄𝒚

𝑪𝒐𝒏𝒄𝒖𝒓𝒓𝒆𝒏𝒕 𝒍𝒊𝒏𝒆𝒔

𝑶𝒓𝒕𝒉𝒐𝒄𝒆𝒏𝒕𝒆𝒓

Mrs. Rivas

𝑪𝒆𝒏𝒕𝒓𝒐𝒊𝒅

𝑪𝒊𝒓𝒄𝒖𝒎𝒄𝒆𝒏𝒕𝒆𝒓

𝑽𝒆𝒓𝒕𝒆𝒙