Question

congruent vs equal
congruent symbol:
congruent means: same shape, same size
tick marks used to show that segments are congruent!
congruent uses letters/name
\\(\overline{dc}\cong\\)
equal symbol:
equal means: equal in measurement (numerically)
numbers used to show that segments are equal
equal uses the number
\\(dc =\\)
\\(de =\\)
segment addition postulate and midpoints (using numbers)

1. fill in the answers for each segment using the information in the diagram below

a) \\(tu=12\\) b) \\(\overline{tv}=\\) c) \\(\overline{tu}\cong\\) d) \\(ru =\\)
recall: midpoint is the middle of the segment. it cuts the segment into two equal parts. a segment can also be bisected by another segment, line, or ray. if you dont have the midpoint given in words or symbolically (tick marks on the picture), then you cannot assume any parts are equal!

1. in the figure below, \\(\overline{ac}\cong\overline{ce}\\) and \\(b\\) is the midpoint of \\(\overline{ac}\\). if \\(cd = 2\\), and \\(ab = 3\\), then find the following:

\\(bc=\\)
\\(ac =\\)
\\(de =\\)
\\(be =\\)
you try: #25 and 26

1. given the diagram below, find the following:

a. \\(uw = 10\\) b. \\(\overline{xy}\cong\\) c. \\(\overline{wy}\cong\\) d. \\(yv = 18\\)

1. given the diagram below, if \\(e\\) is the midpoint of \\(\overline{ab}\\), and \\(ab = 28\\), then what is the length of \\(cb\\)?

Explanation:

Step1: Problem 23a: TU length

TU is given as 12.

Step2: Problem 23b: TV calculation

TV = TU + UV = 12 + 24 = 36

Step3: Problem 23c: TW calculation

TW = TU + UV + VW = 12 + 24 + 18 = 54

Step4: Problem 23d: RU calculation

RU = RS + ST + TU = 12 + 24 + 12 = 48

Step5: Problem 24a: BC length (midpoint)

B is midpoint of AC, so BC = AB = 3

Step6: Problem 24b: AC length

AC = AB + BC = 3 + 3 = 6

Step7: Problem 24c: DE calculation (congruent segments)

AC ≅ CE = 6, CE = CD + DE → 6 = 2 + DE → DE = 4

Step8: Problem 24d: BE calculation

BE = BC + CD + DE = 3 + 2 + 4 = 9

Step9: Problem 25a: UW length

UW = UV + VW = 5 + 5 = 10

Step10: Problem 25b: XY congruent segment

XY = 8, TU = 8, so XY ≅ TU

Step11: Problem 25c: WY congruent segment

WY = WX + XY = 5 + 8 = 13; TV = TU + UV = 8 + 5 = 13, so WY ≅ TV

Step12: Problem 25d: YV length

YV = XY + WX + VW = 8 + 5 + 5 = 18

Step13: Problem 26: CB length (midpoint)

E is midpoint, AE = EB = 14. Tick marks imply AC = CE = 7, so CB = CE + EB = 7 + 14 = 21

Answer:

23a. 12
23b. 36
23c. 54
23d. 48

1. BC = 3, AC = 6, DE = 4, BE = 9

25a. 10
25b. XY ≅ TU
25c. WY ≅ TV
25d. 18

1. 21