Practice 2A 1. Which point in the diagram must be a midpoint?
2. A median is a segment in a triangle that goes from a
vertex to the midpoint of the opposite side. Which
segment in the diagram must be a median?
3. A perpendicular bisector is perpendicular to a segment
at its midpoint. Which segment in the diagram must be a
perpendicular bisector?
4. If DB=4x+5 and DC=2x+11, what is the value of x?
5. If EB=4x-5 and EC=3x+10, then what is the value of
x?
Practice 2B 1. Ray MO bisects ∠LMN, m∠LMO=8x−23, and 3. Ray SQ bisects ∠RST, and m∠RSQ=3x−9. Write an m∠NMO=2x+37. Solve for x and find m∠LMN. The diagram is not to scale. 2. Ray MO bisects ∠LMN, m∠LMN=5x−23, expression for ∠RST. The diagram is not to scale. A. 6x-­‐9 B. 6x-­‐18 C. 3x-­‐9 D. 1.5x-­‐4.5 m∠LMO=x+32. Find m∠NMO. The diagram is not to scale. 4. Which statement can you conclude is true from the given information? A. AJ=BJ B. ∠IAJ is a right angle. C. IJ=JK D. A is the midpoint of segment IK. 5. Which statement is not necessarily true? A. DK=KE B. line DE ⊥ line JL C. K is the midpoint of segment JL. D. DJ=DL Practice 2C 1. The length of DE is shown. What other length can you determine for this diagram? A. EF = 12 B. DG = 12 C. DF = 24 D. No other length can be determined. 3. Segment DF bisects ∠EDG. Find the value of x. The diagram is not to scale. Practice 2D 1. In ΔABC, G is the centroid and BE = 9. Find BG and GE. 2. Q is equidistant from the sides of ∠TSR. Find the value of x. The diagram is not to scale. 4. Q is equidistant from the sides of 5. Ray DF bisects ∠EDG. Find FG. The ∠TSR. Find m∠RST. The diagram is not diagram is not to scale. to scale. 2. Name a median for ΔABC. 4. Where can the medians of a triangle intersect? I. inside the triangle II. on the triangle III. outside the triangle A. I only B. III only C. I or III only D. I, II, and III 3. Find the length of AB, given that segment DB is a median of the triangle and AC=26. 5. Where can the lines containing the altitudes of an obtuse triangle intersect? I. inside the triangle II. on the triangle III. outside the triangle A. I only B. I or II only C. III only D. I, II, or III Practice 2E 1. Where is the center of the largest circle that you could draw inside a given triangle? A. the point of concurrency of the altitudes of the triangle B. the point of concurrency of the perpendicular bisectors of the sides of the triangle C. the point of concurrency of the bisectors of the angles of the triangle D. the point of concurrency of the medians of the triangle 2. Where can the bisectors of the angles of an obtuse triangle intersect? I. inside the triangle II. on the triangle III. outside the triangle A. I only B. III only C. I or III D. I, II, or III 3. For a triangle, list the respective names of the points of concurrency of • perpendicular bisectors of the sides • bisectors of the angles • medians • lines containing the altitudes. 4. Which diagram shows a point P an equal distance from points A, B, and C? A. B. C. D. 5. In ΔABC, centroid D is on median AM. AD=x+4 and DM=2x−4. Find AM.