13) Name the point of concurrency of all three altitudes of a triangle?
14) \(\triangle ROB\) is obtuse. Name two points of concurrency that lie outside the triangle.
15) \(\triangle POR\) is a right triangle. Name the point of concurrency that lies on the vertex of the right angle.
16) On the same right triangle \(\triangle POR\), name the point of concurrency that lies on the midpoint of the hypotenuse.
17) \(\triangle TER\) is equilateral. Describe the location of the circumcenter, incenter, centroid and orthocenter.
18) What two points of concurrency always lie inside the triangle?
14) \(\triangle ROB\) is obtuse. Name two points of concurrency that lie outside the triangle.
15) \(\triangle POR\) is a right triangle. Name the point of concurrency that lies on the vertex of the right angle.
16) On the same right triangle \(\triangle POR\), name the point of concurrency that lies on the midpoint of the hypotenuse.
17) \(\triangle TER\) is equilateral. Describe the location of the circumcenter, incenter, centroid and orthocenter.
18) What two points of concurrency always lie inside the triangle?
19) Given \(\overline{XO}\) is the \(\perp\) bis of \(\overline{AC}\), \(\overline{YO}\) is the \(\perp\) bis of \(\overline{AB}\),
\(\overline{ZO}\) is the \(\perp\) bis of \(\overline{BC}\) a) What is the name of the point of concurrency of point \(O\)? b) What is the relationship between \(\triangle OZB\) and \(\triangle OZC\)? Give a reason (SSS, SAS, ASA, AAS, or HL) c) Find \(OB\) d) Find \(OC\) e) Find \(OA\) |
22) Find the circumcenter point for \(\triangle ABC\) whose vertex points are \(A(3, 6), B(3, 0),\) and \(C(7, 8)\).
Hint: use GeoGebra or Desmos.
Hint: use GeoGebra or Desmos.
23) Given: \(\overrightarrow{DP}\) bisects \(\angle EDF\), \(\overrightarrow{EQ}\) bisects \(\angle DEF\),
\(\overrightarrow{FR}\) bisects \(\angle DFE\), \(DK = 15\), \(DV = 12\) a) What is the point of concurrency for point \(K\)? b) What is the relationship of \(\triangle DKV\) and \(\triangle DKU\)? Give a reason (SSS, SAS, ASA, AAS, or HL) c)Find \(DV\) d) Find \(DU\) e) Find \(KW\) |
26) Find the incenter point for \(\triangle ABC\) whose vertex points are \(A(-3, -1), B(6, 11),\) and \(C(22, -1)\).
Hint: use GeoGebra or Desmos
Hint: use GeoGebra or Desmos
27) Given: \(G\) is the midpoint of \(\overline{LN}\), \(H\) is the midpoint of \(\overline{LK}\),
\(J\) is the midpoint of \(\overline{NK}\). a) What is the name of the point of concurrency for point \(T\)? b) If \(LT = 9\), find \(TJ\). c) If \( TH = 2.5\), find \(NT\). d) If \(LH = 7.1\), find \(HK\). e) If \(KG = 12.3\), find \(KT\) and \(TG\) |
28) Your friend from California is moving to Naperville and will be joining you at NCHS! She tells you that both her parents got new jobs. Her mother will be working at Nike Sports Complex near the corner of Mill and Diehl. Her father will be working at Benedictine University. Suggest a location for your friend to start looking for a house so that the distance to each of the three locations is the smallest. Explain why this location is the best.
29) Place your warehouse so that you can supply each of the three locations of your coffee business with minimal travel distance.
30) The triangle below closely resembles three Chicago Interstates (I-90, I-294, and I-290). Suggest a location to store road salt to service the three interstates so that access to the three roadways is the minimalist. Explain why this location is the best.
Review
Determine what information can be concluded from the diagrams, the reason why each pair of triangles are congruent (name the postulate), and identify the congruence transformation that maps the triangles to each other.
Determine what information can be concluded from the diagrams, the reason why each pair of triangles are congruent (name the postulate), and identify the congruence transformation that maps the triangles to each other.