## 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, Area_{ABM}/Area_{ACM} ?

(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 100

^{o}, angle BMD is 40

^{o}and angle CME is 60

^{o}. What is the value of angle CMD?

*Figure not drawn to scale*

(a) 20

^{o}

(b) 30

^{o}

(c) 40

^{o}

(d) 50

^{o}

(e) 80

^{o}

Answer: If angle AMB is 100

^{o}, then angle BME is 180

^{o}– 100

^{o}= 80

^{o}

BMC + CMD = 40

^{o}

BMC + CMD + DME = 80

^{o}

If we subtract the 2 equations, DME = 40

^{o}

CMD + DME = 60

^{o}

BMC + CMD + DME = 80

^{o}

If we subtract the 2 equations, BMC = 20

^{o}

CMD = BME – BMC – DME = 80

^{o}– 40

^{o}– 20

^{o}= 20

^{o}