Question

Which ray is a bisector of angle A B C?

Select one:
A. stack B C with rightwards arrow on top
B. stack B D with rightwards arrow on top
C. stack B A with rightwards arrow on top
D. stack B F with rightwards arrow on top

What is GH?

Select one:
A. 5
B. 10
C. 15
D. 25

Answer 1

Answers:

Ray BD is the bisector (choice B)

GH is 15 units long (choice C)

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Explanations:

Use a marker/pen of a different color to highlight angle ABC so its easier to see. Check out the diagram below. The only ray in the interior of this angle is ray BD. The bisector must always be in the interior. The angle markers for angle ABD and DBC are the same indicating they are the same measure; therefore, ray BD bisects angle ABC.

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Segments IG and GH are the same length because they share the same single tickmark. Their lengths are shown as 3x and 5x-10. Set the algebraic expressions equal to one another. Solve for x. Then use this x value to find GH

IG = GH

3x = 5x-10

3x-5x = -10

-2x = -10

x = -10/(-2)

x = 5

GH = 5x-10

GH = 5*5-10

GH = 25-10

GH = 15

note that IG = 3x = 3*5 = 15 as well