2. In ABC, the measure of angle B is twice the measure of angle A. Angle C measures three times the measure of angle A. If AC = 26, find AB.


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1 2009 FGCU Mathematics Competition. Geometry Individual Test 1. You want to prove that the perpendicular bisector of the base of an isosceles triangle is also the angle bisector of the vertex. Which postulate/theorem can NOT be used in your proof? HL SSS SSA SAS 2. In ABC, the measure of angle B is twice the measure of angle A. Angle C measures three times the measure of angle A. If AC = 26, find AB (52/3) In ABC, AD = 8 and DB = 2. Find AC In right ABC, altitude is drawn to the hypotenuse. CD is the geometric mean of and. AC and BC AD and BD AB and DB AB and AD 5. In ABC, is the altitude to side. If AD = 1 and DB =, find BC that will make ABC a right triangle
2 6. In parallelogram ABCD, 1 2. The reason for ABC and DEF being congruent is. SSA AAS SAS ASA 7. Given: QEL DPC Q E D P What must also be true? DPC QEL QE DP E D C L All of the above 8. An equilateral triangle has. no congruent sides only two congruent sides all congruent sides 9. Given: BSH m B = 26 m S = 90 m H = 6 What is BSH? an equiangular triangle an acute triangle a right triangle an obtuse triangle
3 10. of a triangle is the angle adjacent to an interior angle of a triangle that is formed when one of the sides of the triangle is extended. An interior angle A scalene A complementary angle A remote interior angle An exterior angle 11. Which of the following statements is NOT true? Q is the vertex of angles PQS, SQR, and PQR. PQS and PQR are adjacent angles. m PQR = m PQS + m SQR T is in the interior of PQS. P is in the exterior of RQS. 12. Points X and Y are on. If AX > BY, then which statement must be true? AY > BX XY < BY AY < BY AY + BX > AB AX < BX 13. Points E, F, and G are. collinear coplanar noncoplanar noncollinear
4 1. If two distinct planes intersect, they intersect in exactly. one plane one point one line two points two lines 15. Which of the following statements is NOT true? Planes X and Y contain both M and N. Points N and P are noncoplanar. Points L, M, N, and P are coplanar. Plane Y and intersect in point L. 16. The measure of each interior angle in a polygon is 120. What is the name of the polygon? heptagon quadrilateral octagon hexagon decagon 17. Polygon G has k sides. How many diagonals can be drawn inside of polygon G? k(k  2) 2 3 (k  2) k(k  2) k(k  3) 2 k(k  2) 3 (k)
5 18. What is the sum of the measures of the interior angles of a pentagon? A statement whose truth is accepted without proof is considered to be a. Geometry Definition Point Theorem Postulate 20. A has position only. It does not have width, height, or length. point ray space rectangle plane 21. How would you write that line segment PK has equal length with line segment OQ? PK = OQ PK = OQ PK OQ PK = OQ PK OQ 22. Which of the following is not true? The diagonals of a rhombus are congruent. The diagonals of a rectangle are congruent. The four sides of a rhombus are congruent. A rectangle has right angles. A rhombus is a parallelogram. The diagonals of a rhombus are perpendicular.
6 23. In ABC, is the perpendicular bisector of and D lies on. Which statement(s) must be true? (I) ABD ACD (II) ABC is equilateral. (III) is the bisector of BAC. I and III only II only I only III only I, II, and III 2. Given: D is in the interior of ABE. E is in the interior of DBF. F is in the interior of EBC. m ABC = 150, m EBC = 9, m ABD = m EBF, m FBC = 2m DBE Which of the following is incorrect? m ABD = 18 m ABF = 9 m FBC = 76 m DBF = In ABC, k is the perpendicular bisector of side and =. Which of the following statements is incorrect? Point D is the circumcenter of ABC. ABC is a right triangle. DAB DBA Point D is the incenter of ABC. 26. X is a point inside triangle ABC. If X is equidistant from and, then X must lie on the. bisector of C perpendicular bisector of median of C altitude to side
7 27. Triangle ABC is a triangle with C at the right angle. If AC = 5, find BC In triangle ABC, the ratio of the measure of angle A to angle B is 1:3. The measure of angle C is half the sum of the measures of angles A and B. If AC = 8, find BC Given circle O with segment AB tangent to the circle at A. If OA = AB, what kind of triangle is OAB? a scalene triangle an isosceles right triangle an equilateral triangle an equilateral acute triangle an isosceles obtuse triangle
8 30. In the figure, the radius for P is r and the radius for Q is R. Which of the following statement is true? Circles P and Q have two common tangents. PQ = R  r PQ = R + r Circles P and Q have four common tangents
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