Triangles in Plane Geometry

Geometry Quiz


Question 1: The average of angles a and b of triangle ABC is equal to 55o. What is the value of angle c?

Question 2: Triangle ABC has MN parallel to BC and AM/AB = 2/3. What is the ratio between the area of triangle AMN and the area of triangle ABC?

Question 3: What is the length of the segment BD in the figure below, if AD is 6cm?
Figure not drawn to scale

Question 4: What percentage of the area of the triangle below is shadowed? All triangles are equilateral.

Question 5: A circle of center O is inscribed in a right isosceles triangle, ABC as seen in the figure above. If side AC is tangent to the circle in point T and the radius of the circle is r, which of the following approximates best the length of the segment BT?

Question 6: In the picture given below, D is a point on the side BC of triangle ABC. Determine which of the following given assumptions are enough to prove that the ABD and ACD triangles are similar.

Question 7: In triangle ABC, MN is the mediator of segment B (MN ⊥ BC and BM = MC). If ∠BNM = α and ∠BAC = 2α, calculate the ratio between the lengths of segments MN and AC as a function of α.

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