# Similarity, Right Triangles and Trigonometry

## Common Core Geometry Questions

This quiz is designed in accordance with the following Common Core State (CCS) standards:

 Question Common Core Standard # 1 G.SRT.1 2 G.SRT.2 3 G.SRT.4 4 G.SRT.5 5 G.SRT.5 6 G.SRT.7 7 G.SRT.8 8 G.SRT.9 + 9 G.SRT.10 + 10 G.SRT.10 +
indicates a modeling standard.
+ indicates a college and career ready standard.

All questions of this quiz illustrate the difficulty of the high school G.SRT standards required for all students, including the college and career ready students.

Question 1: Suppose we apply dilation by a factor of 1.2, centered at the origin of the Cartesian system, to the segment AB in the figure below. The coordinates of point A are (0, 4) and the coordinates of point B are (3, 0). Locate the images A' and B' of the points A and B under this dilation and calculate the distance d = A'B'.

Question 2: 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 3: Triangle ABC in the picture below has ∠ABC = 60o and ∠BCA = 40o. If AD, BE and CF are the bisectors of the triangle, which of the following pairs of triangles are similar:

Question 4: The line segment BE intersects rectangle ABCD in point F. What is the area of triangle AFE if AB = 6, BC = 20 and FD = 8?

Question 5: BD is one of the diagonals of the trapezoid ABCD. If triangle ABD is similar to triangle DCB, which of the following is true:

Question 6: Select the correct relationship between the angles a and b of the right triangle ABC, in the figure below.

Question 7: A circle is inscribed in the right triangle ABC from the picture below. What is the radius r of the circle if AB = 4 cm?

Question 8: Calculate the area A of triangle ABC in the figure below. The lengths of the sides AB and BC are AB = 4 and BC = 5.

Question 9: Triangle ABC in the figure below has a = 20, b= 30 and ∠CAB = 30°. Which of the following is the closest to the value of angle BCA?

Question 10: If AB = a, AC = 2a and ∠BAC = 60°, calculate the sum of squares of the sides of triangle ABC as a function of a.

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