Question

ΔAXY is similar to ΔABC.
triangles ABC and AXY that share vertex A where point X is between points A and B and point Y is between points A and C
Which of the following expressions could be used to determine the length of segment AB?
A. AB=AX times AC over AY
B. AB=AX times AY over AC
C. AB=AY
D. AB=AX

Answer 1

The expression that can be used to determine the length of segment AB is: A. AB = (AX × AC)/AY.

When are Two Triangles Similar to Each Other?

When the corresponding sides of two triangles have ratios that are equal, or have corresponding side lengths that are proportional to each other, both triangles are considered similar triangles to each other.

Given that triangles AXY and ABC are similar triangles sharing a common vertex A, therefore, the corresponding sides will have equal ratio which can be expressed as:

AB/AX = BC/XY = AC/AY

To find the length of segment AB, we would do the following:

AB/AX = AC/AY

Cross multiply

(AB)(AY) = (AX)(AC)

Divide both sides by AY

(AB × AY)/AY = (AX × AC)/AY

AB = (AX × AC)/AY

The expression we can use to find the length of segment AB can be:

A. AB = (AX × AC)/AY

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