Geometry Chap 5

In a triangle, a segment connecting the midpoints of two sides of the triangle is called a _____.

• shortcut

• midsegment

• centroid

• vertex

Answer explanation

In a triangle, a segment connecting the midpoints of two sides is known as a midsegment. It is parallel to the third side and half its length, making 'midsegment' the correct term.

Point Q represents which point of concurrency?

• centroid

• incenter

• orthocenter

• circumcenter

Answer explanation

Point Q represents the centroid, which is the point of concurrency of the medians of a triangle. The centroid is the balance point and divides each median into a 2:1 ratio.

Tags

CCSS.HSG.C.A.3

Point P represents which point of concurrency?

• centroid

• incenter

• orthocenter

• circumcenter

Answer explanation

Point P represents the incenter, which is the point of concurrency of the angle bisectors of a triangle. It is equidistant from all sides of the triangle, making it the correct choice.

Tags

CCSS.HSG.C.A.3

Point P represents which point of concurrency?

• centroid

• incenter

• orthocenter

• circumcenter

Answer explanation

Point P represents the circumcenter, which is the point where the perpendicular bisectors of a triangle intersect. It is equidistant from all three vertices of the triangle, making it the correct choice.

Tags

CCSS.HSG.C.A.3

Point T represents which point of concurrency?

• centroid

• incenter

• orthocenter

• circumcenter

Answer explanation

Point T represents the orthocenter, which is the point where the altitudes of a triangle intersect. Unlike the centroid, incenter, and circumcenter, the orthocenter is specifically related to the triangle's heights.

Tags

CCSS.HSG.C.A.3

Point M represents which point of concurrency?

• centroid

• incenter

• orthocenter

• circumcenter

Answer explanation

Point M represents the centroid, which is the point of concurrency of the medians of a triangle. The centroid is the balance point and divides each median into a 2:1 ratio.

Tags

CCSS.HSG.CO.C.10

Point W represents which point of concurrency?

• centroid

• incenter

• orthocenter

• circumcenter

Answer explanation

Point W represents the orthocenter, which is the point where the three altitudes of a triangle intersect. This distinguishes it from the centroid, incenter, and circumcenter, which are defined by different triangle properties.

Tags

CCSS.HSG.C.A.3

Point L represents which point of concurrency?

• centroid

• incenter

• orthocenter

• circumcenter

Answer explanation

Point L represents the orthocenter, which is the point where the altitudes of a triangle intersect. This distinguishes it from the centroid, incenter, and circumcenter, which are defined by different triangle properties.

Tags

CCSS.HSG.C.A.3

Which point of concurrency is the intersection of the medians of the triangle?

• centroid

• incenter

• orthocenter

• circumcenter

Answer explanation

The centroid is the point of concurrency where the three medians of a triangle intersect. It is the center of mass and divides each median into a 2:1 ratio, making it the correct answer.

Tags

CCSS.HSG.C.A.3

Which point of concurrency is the intersection of the altitudes of the triangle?

• centroid

• incenter

• orthocenter

• circumcenter

Answer explanation

The orthocenter is the point of concurrency where the altitudes of a triangle intersect. In contrast, the centroid is where the medians meet, the incenter is where the angle bisectors intersect, and the circumcenter is where the perpendicular bisectors meet.

Tags

CCSS.HSG.C.A.3