Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Mu Alpha Theta January Regional Geometry Team Questions o o 1. In the ABC, A + B = 130 and A + C = 110 . How large is A? 2. The sum of the two exterior angles formed by extending the hypotenuse of a right triangle is how many degrees? 3. Find the number of degrees in the angle formed by two diagonals drawn from the same vertex of a regular pentagon. 4. In a square of base 5, a 3-4-5 right triangle is positioned as shown below. Determine the distance x: E A B F 4 D 5. 3 C 5 o In the triangle ABC, AC=BC and AD bisects angle A. If ADC=114 , then what is the measure of C? 6. The bases of an isosceles trapezoid are AB=15 inches and DC=9 inches respectively; each leg is 5 inches. Find the length of a diagonal. D A C B 7. The perimeter of a rhombus is 80 cm, and one diagonal is 14 cm long. Find the length of the other diagonal. 8. If the sum of the interior angles of a polygon equals four times the sum of the exterior angles, how many sides does the polygon have? 9. If the segments of the hypotenuse of a right triangle made by the altitude to the hypotenuse are 3 and 12, find the altitude. Mu Alpha Theta January Regional Geometry Team Questions 10. Suppose the medians AA' and BB' of triangle ABC intersect at right angles. If BC = 3 and AC = 4, what is the length of side AB? 11. The sides of a right triangle are a, a+d, and a+2d, with a and d both positive. Find the ratio of a to d. 12. HIJK and DCBA are congruent parallelograms, with altitude HL. HK=10 cm, LJ = 8 cm, 2 and the area of ABCD is 112cm . What is the length of altitude DM? I H C D 10 M K A L B J 8 13 The coordinates of the vertices of ABC are A(-5,1), B(-2,3) and C(-4,7). The triangle is reflected over the line x=2. What is the sum of the x-coordinates of the images of points A, B, and C? 14. An isosceles triangle has lengths 6x+40, 4x+104, and 7x-23. What is the greatest possible perimeter? 15. Two congruent regular polygons are placed side-by-side so they share a common side. The angle formed between the polygons is a right angle. How many sides does each polygon have?