Common Core Geometry, June 2015, Questions 30
30. After a reflection over a line, Triangle A'B'C' is the image of Triangle ABC. Explain why triangle ABC is congruent to triangle A'B'C'.
A reflection is a rigid motion that preserves distance. Since the distance between the points in the same AB = A'B', BC = B'C' and CA = C'A'. The sides are congruent, so the two triangles are congruent.
Common Core Geometry, June 2015, Questions 31
31. A flagpole casts a shadow 16.60 meters long. Tim stands at a distance of 12.45 meters from the base of the flagpole, such that the end of Tim's shadow meets the end of the flagpole's shadow. If Tim is 1.65 meters tall, determine and state the height of the flagpole to the nearest tenth of a meter.
Tim and his shadow form a triangle that is similar to the flagpole and its shadow. The ratios of the shadows to the heights are proportional.
Be careful! Tim is standing 12.45 meters from the flagpole. That means his shadow is only 16.60 - 12.45 = 4.15 meters long. Don't use the incorrect number.
So 1.65 / 4.15 = x / 16.60
Cross multiply: 4.15x = (1.65)(16.60)
Divide: x = (1.65)(16.60)/4.15 = 6.6 meters
The flagpole is 6.6 meters high.
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