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Geometry Quiz 5-1, 5-3, 5-4 Version B Name:___________________________ 1. Matching – match the definition with the correct corresponding term. _____1. equidistant _____2. Angle Bisector Theorem _____3. Perpendicular Bisector Theorem _____4. median of a triangle _____5. altitude of a triangle _____6. centroid of a triangle _____7. orthocenter of a triangle _____8. midsegment of a triangle a. If a point is on the bisector of an angle, then it is equidistant from the sides of the angle. b. Where the medians of a triangle intersect. c. A perpendicular segment from a vertex of a triangle to the line containing the opposite side. d. When a point is the same distance from two or more objects. e. Where the altitudes of a triangle intersect. f. A segment that joins the midpoints of two sides of a triangle. g. A segment whose endpoints are a vertex of a triangle and the midpoint of the opposite side. h. If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment. 2. Find the following: a. EF ________ b. AB ________ c. mEDF ________ 3. What is the distance RQ across the pond? Explain how you know and be sure to state the theorem that supports your explanation. Find each measure. 4. BC = 5. 6. x= DC = 7. In ∆XYZ, ZL = 48, NP = 12. Find the following. a. ZP ________ b. PY ________ c. NY ________ 8. Melissa cuts a triangle with vertices at coordinate (0, 12), (8, 1), and (16, 20). At what point should she place the tip of a pencil to balance a triangle (what is the centroid)? 9. The vertices of ∆ABC are A(6, 10), B(2, 4), and C(8, 8). R is the midpoint of segment AB and S is the midpoint of segment AC. a. Find the coordinates of point R and point S. b. Calculate the slope of segments RS and BC. c. Calculate the length of segments RS and BC. (Hint: use the distance formula.) d. Using slope and segment length, explain how you know that segment RS is a midsegment of ∆ABC.