Points of Concurrency Regents Exam Questions

• the angle bisectors of ΔABC

• the medians to the sides of ΔABC

• the altitudes to the sides of ΔABC

• the perpendicular bisectors of the sides of ΔABC

Tags

CCSS.HSG.C.A.3

In the diagram below of ∆ABC, CD is the bisector of ∡BCA, AE is the bisector of ∡CAB, and BG is drawn.

Which statement must be true?

• DG=EG

• AG=BG

• ∡AEB ≅ ∡AEC

• ∡DBG≅∡EBG

Tags

CCSS.HSG.C.A.3

Answer the following question given B is the incenter of ∆FEC.

Mathematical Equivalence

ON

Tags

CCSS.HSG.C.A.3

Answer the question given triangle ABC.

Mathematical Equivalence

ON

Tags

CCSS.HSG.CO.C.9

This construction represents how to find the intersection of

• the angle bisectors of ΔABC

• the medians to the sides of ΔABC

• the altitudes to the sides of ΔABC

• the perpendicular bisectors of the sides of ΔABC

Tags

CCSS.HSG.C.A.3

If the altitudes of a triangle meet at one of the triangle's vertices, then the triangle is

• a right triangle

• an acute triangle

• an obtuse triangle

• an equilateral triangle

Tags

CCSS.HSG.CO.C.10

In which triangle do the three altitudes intersect outside the triangle?

• a right triangle

• an acute triangle

• an obtuse triangle

• an equilateral triangle

Tags

CCSS.HSG.CO.C.10

For a triangle, which two points of concurrency could be located outside the triangle?

• incenter and centroid

• centroid and orthocenter

• incenter and circumcenter

• circumcenter and orthocenter

Tags

CCSS.HSG.C.A.3

Triangle ABC is graphed on the set of axes. What are the coordinates of the point of intersection of the medians of ABC?

• (-1, 2)

• (-3, 2)

• (0, 2)

• (1, 2)

Tags

CCSS.HSG.CO.C.10

The vertices of the triangle in the diagram below are A(7,9), B(3,3), and C(11,3). What are the coordinates of the centroid of ABC?

• (5, 6)

• (7, 3)

• (7, 5)

• (9, 6)