The length of AB when A'B' is 8 is 12
The measurement of B' when angle B is 40° is also 40°
The measurement of A' when A is 80° is also 80°
The measurement of C using AB is 60°
What are similar triangles?
Similar triangles are triangles that have the same angles and the ratio of their corresponding sides are equal.
Analysis:
ΔCA'B' is similar to ΔCAB.
Which means [tex]\frac{A'B'}{AB}[/tex] = [tex]\frac{CB'}{CB}[/tex] = [tex]\frac{CA'}{CA}[/tex]
A'B' = 8, CA' = 4, CA = 6
[tex]\frac{8}{AB}[/tex] = [tex]\frac{4}{6}[/tex]
4AB = 8 X 6
AB = 48/4 = 12
Line BA nd B'A' are parallel lines joined by two transversals BC and CA.
So, ∠B = ∠B' = 40°( corresponding angles are equal)
Also, ∠A = ∠A' = 80° ( corresponding angles are equal)
∠A + ∠B +∠C = 180( sum of angles in a triangle)
80 + 40 + ∠C = 180
120 + ∠C = 180
∠C = 180 - 120 = 60°
In conclusion,
The length of AB when A'B' is 8 is 12
The measurement of B' when angle B is 40° is also 40°
The measurement of A' when A is 80° is also 80°
The measurement of C using AB is 60°.
Learn more about similar triangles: brainly.com/question/2644832
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