test

TEST

In this section a reader will have a chance to check his/her knowledge of the material presented in tutorial. Below are given eight test problems. In order to solve them a reader is supposed to use main definitions and results discussed in the tutorial. Each problem is worth 10 points. A reader can make 3 attempts to solve a problem. The first successful attempt is worth 10 points, the second successful attempt is worth 7 points and the third successful attempt is worth 4 points. In case a person needs more than 3 attempts in order to get the correct answer, no points will be given for this problem. After the completion of the test a reader will be given the total score for the test. The total score is considered to be perfect if it is between 65 and 80 points inclusive, good if it is between 50 and 64 points inclusive, satisfactory if it is between 35 and 49 points inclusive and unsatisfactory otherwise.

PROBLEM SET

Problem 1. Find the degree measure of the angle ABC on the picture below if

Problem 2. Suppose that lines AB and DE are parallel and degree measures of angles BAC and EDC are equal to 25 and 45 degrees respectively. Find the degree measure of the angle ACD.

Problem 3. ABCD is a trapezoid with BC parallel to AD. Suppose that AM = MB, ME is parallel to CD and CD is equal to 6 inches. Find the length of ME.

Problem 4. Let AMK be a triangle with AM = 6 inches and MK = 4 inches. Let MD be perpendicular to AK. What is the length of AD if DK = inches?

Problem 5. Let ABC be an arbitrary triangle and let AM and CN be two angle bisectors. If O is the point of intersection of AM and CN and the degree measure of the angle AOC is equal to 130 degrees, what is the degree measure of the angle ABC?

Problem 6. Suppose that ABC is a right triangle with the right angle C. If AC = 6 inches and the degree measure of the angle ABC is equal to 45 degrees, find the length of BC.

Problem 7. ABCD is a rhombus with diagonals AC and BD. Suppose that O is the point of intersection of AC and BD and OB = 6 inches. Let K be an arbitrary point on the ray CA outside ABCD. If KD = 10 inches, what is the length of KO?

Problem 8. Let O be a circle with diameter AC. Find the degree measure of the inscribed angle BDC if the degree measure of the angle ACB is equal to 40 degrees.