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Examples of SAT Reasoning Geometry Problems

Question: The median m divides the ABC triangle in 2 triangles, ABM and ACM. What is the ratio between the areas of the 2 triangles, AreaABM/AreaACM ?
sat, geometry, triangle
(a) 1
(b) 1/2
(c) 2
(d) It cannot be determined from the information given
(e) 3

Answer: The areas of the 2 triangles will be equal because they are both (1/2) · h ·(BC/2), where h is the altitude. The correct answer is (a).



Question: In the figure below, angle AMB is 100o, angle BMD is 40o and angle CME is 60o. What is the value of angle CMD?
Figure not drawn to scale
sat, geometry, problem, angles
(a) 20o
(b) 30o
(c) 40o
(d) 50o
(e) 80o

Answer: If angle AMB is 100o, then angle BME is 180o – 100o = 80o
BMC + CMD = 40o
BMC + CMD + DME = 80o
If we subtract the 2 equations, DME = 40o
CMD + DME = 60o
BMC + CMD + DME = 80o
If we subtract the 2 equations, BMC = 20o
CMD = BME – BMC – DME = 80o – 40o – 20o = 20o

 

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